Important Questions for CBSE Class 8 Maths Chapter 12 - Exponents and Powers

Very Short Answer Questions                                                   1 Marks

1. \[\mathrm{3}\] multiplied fifteen times is written as?

Ans:

\[3\] Multiplied for fifteen times is written as 

\[3\times 3\times 3\times 3\times 3\ldots 15 times={{3}^{15}}\]

Answer will be \[{{3}^{15}}\]

2. What is the base of the exponent \[{{\mathrm{6}}^{\mathrm{9}}}\]?

\[\begin{align} & \mathrm{(a)6} \\  & \mathrm{(b)2} \\  & \mathrm{(c)9} \\  & \mathrm{(d)None} \\  \end{align}\]

Ans:

The base of the exponent \[{{6}^{9}}\] is \[6\]

3. Find the missing number \[{{\mathrm{7}}^{\mathrm{5}}}\mathrm{=}\dfrac{\mathrm{1}}{{{\mathrm{7}}^{\square }}}\]?

\[\begin{align} & \mathrm{(a)2} \\  & \mathrm{(b)-5} \\  & \mathrm{(c)1} \\  & \mathrm{(d)None} \\  \end{align}\]

Ans:

The missing number should be  \[-5\]

So the answer will be \[{{7}^{5}}=\dfrac{1}{{{7}^{-5}}}\]

4. Find the value of  \[{{\left( {{\mathrm{5}}^{\mathrm{2}}} \right)}^{\mathrm{2}}}\]

\[\begin{align} & \mathrm{(a)125} \\  & \mathrm{(b)625} \\  & \mathrm{(c)25} \\  & \mathrm{(d)0} \\  \end{align}\]

Ans:

The solution will be

\[\begin{align} & {{\left( {{5}^{2}} \right)}^{2}}={{5}^{4}} \\  & {{\left( {{5}^{2}} \right)}^{2}}=5\times 5\times 5\times 5 \\  & {{\left( {{5}^{2}} \right)}^{2}}=625 \\  \end{align}\]

5. Find the value of \[\mathrm{x}\], when \[{{\mathrm{2}}^{\mathrm{x}}}\mathrm{=}{{\mathrm{4}}^{\mathrm{4}}}\]

\[\begin{align} & \mathrm{(a)x=6} \\  & \mathrm{(b)x=2} \\  & \mathrm{(c)x=8} \\  & \mathrm{(d)x=-5} \\  \end{align}\]

Ans:

The solution will be 

\[{{2}^{x}}={{4}^{4}}\]

\[\begin{align} & {{4}^{4}}={{\left( {{2}^{2}} \right)}^{4}} \\  & {{4}^{4}}={{2}^{8}} \\  \end{align}\]

\[{{2}^{x}}={{2}^{8}}\]

\[x=8\]

So the answer will be \[x=8\]

6. Find the value of \[{{\left( {{\mathrm{2}}^{\mathrm{11}}}\mathrm{+}{{\mathrm{6}}^{\mathrm{2}}}\mathrm{-}{{\mathrm{5}}^{\mathrm{1}}} \right)}^{\mathrm{0}}}\]

\[\begin{align} & \mathrm{(a)0} \\  & \mathrm{(b)-1} \\  & \mathrm{(c)1} \\  & \mathrm{(d)None} \\  \end{align}\]

Ans:

The solution will be 

\[\begin{align} & {{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}={{\left( anything \right)}^{0}} \\  & {{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}=1 \\  \end{align}\]

So the solution will be 

\[{{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}=1\]

7.\[{{\mathrm{I}}^{\mathrm{3}}}\mathrm{+}{{\mathrm{I}}^{\mathrm{-3}}}\mathrm{=?}\] What is the solution?

\[\begin{align} & \mathrm{(a)2} \\  & \mathrm{(b)3} \\  & \mathrm{(c)-3} \\  & \mathrm{(d)None} \\  \end{align}\]

Ans:

The solution will be 

\[\begin{align} & {{I}^{3}}+{{I}^{-3}}=\left( I\times I\times I \right)+\dfrac{1}{\left( I\times I\times I \right)} \\ & {{I}^{3}}+{{I}^{-3}}=\left( -I \right)+\dfrac{1}{\left( -I \right)} \\  & {{I}^{3}}+{{I}^{-3}}=\dfrac{-1+1}{\left( -I \right)} \\  & {{I}^{3}}+{{I}^{-3}}=0 \\  \end{align}\]

So the solution is (d)

Short Answer Questions                                                          2 Marks

8. Follow the pattern and complete

Ans:

The pattern for the solution is square root of the numbers which continue as 

\[\begin{align} & 1234321={{1111}^{2}} \\  & 123454321={{11111}^{2}} \\ \end{align}\]

9. If \[{{\mathrm{2}}^{\mathrm{x}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{5}}^{\mathrm{x}}}\mathrm{=1000}\] then \[\mathrm{x=?}\]

Ans:

For solving we will just factorise 

\[\begin{align} & {{2}^{x}}\times {{5}^{x}}=1000 \\  & {{2}^{x}}\times {{5}^{x}}=5\times 5\times 5\times 2\times 2\times 2 \\  & {{2}^{x}}\times {{5}^{x}}={{2}^{3}}\times {{5}^{3}} \\  & x=3 \\ \end{align}\]

10.Find\[{{\mathrm{3}}^{\mathrm{4}}}\mathrm{+}{{\mathrm{4}}^{\mathrm{3}}}\mathrm{+}{{\mathrm{5}}^{\mathrm{3}}}\] and give the answers in cube 

Ans:

Solve the expression 

\[\begin{align} & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=27+64+125 \\  & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=216 \\  & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=6\times 6\times 6 \\  & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}={{6}^{3}} \\  \end{align}\]

11. Find the missing number \[\mathrm{x}\] in  \[{{\mathrm{5}}^{\mathrm{2}}}\mathrm{+}{{\mathrm{x}}^{\mathrm{2}}}\mathrm{=1}{{\mathrm{3}}^{\mathrm{2}}}\]

Ans:

Solve the expression

\[\begin{align} & {{5}^{2}}+{{x}^{2}}={{13}^{2}} \\  & 25+{{x}^{2}}=169 \\  & {{x}^{2}}=144 \\  & x=\sqrt{144} \\  & x=12 \\  \end{align}\]

12. Simplify in exponent form \[\left( {{\mathrm{3}}^{\mathrm{4}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{2}}} \right)\mathrm{ }\!\!\div\!\!\text{ }{{\mathrm{3}}^{\mathrm{-4}}}\]

Ans:

Solve the expression 

\[\begin{align} & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}=\dfrac{{{3}^{4+2}}}{{{3}^{-4}}} \\  & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}=\dfrac{{{3}^{6}}}{{{3}^{-4}}} \\  & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}={{3}^{6+4}} \\  & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}={{3}^{10}} \\  \end{align}\]

 13. Expand 

\[\begin{align} & \mathrm{(a)1526}\mathrm{.26} \\  & \mathrm{(b)8379} \\ \end{align}\]Using exponents

Ans:

Solve in exponential form 

\[\begin{align} & (a)1526.26=1\times {{10}^{3}}+5\times {{10}^{2}}+2\times {{10}^{1}}+6\times {{10}^{\circ }}+2\times {{10}^{-1}}+6\times {{10}^{-2}} \\  & (b)8379=8\times {{10}^{3}}+3\times {{10}^{2}}+7\times {{10}^{1}}+9\times {{10}^{0}} \\ \end{align}\]

14. Simplify using laws of exponents

\[\begin{align} & \mathrm{(a)}\dfrac{\mathrm{1}}{\mathrm{9}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{5}}} \\  & \mathrm{(b)}{{\mathrm{5}}^{\mathrm{a}}}\mathrm{ }\!\!\times\!\!\text{ 2}{{\mathrm{5}}^{\mathrm{b}}} \\  \end{align}\]

Ans:

Solve in exponential form 

\[\begin{align} & (a)\dfrac{1}{9}\times {{3}^{5}}=\dfrac{{{3}^{5}}}{9}=\dfrac{{{3}^{5}}}{{{3}^{2}}}={{3}^{5-2}}={{3}^{3}}=27 \\  & (b){{5}^{a}}\times {{25}^{b}}={{5}^{a}}\times {{\left( {{5}^{2}} \right)}^{b}}={{5}^{a}}\times {{5}^{b}}={{5}^{a+2b}} \\  \end{align}\]

15. Express the following number as a product of powers of prime factors.

\[\begin{align} & \mathrm{(a)1225} \\  & \mathrm{(b)3600} \\  \end{align}\]

Ans:

Solve in exponential form 

\[\begin{align} & (a)1225=5\times 5\times 7\times 7 \\  & 1225={{5}^{2}}\times {{7}^{2}} \\  \end{align}\]

\[\begin{align} & (b)3600=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5 \\  & 3600={{2}^{4}}\times {{3}^{2}}\times {{5}^{2}} \\  \end{align}\]

16. Express the following large no’s in its scientific notation. 

\[\begin{align} & \mathrm{(a)650200000000} \\  & \mathrm{(b)301000000} \\ \end{align}\]

Ans:

Solve in exponential form

\[(a)650200000000=6.502\times {{10}^{11}}\] 

\[(b)301000000=3.01\times {{10}^{8}}\]

17. Express the following in expanded form \[\begin{align} & \mathrm{(a)1}\mathrm{.682 }\!\!\times\!\!\text{ 1}{{\mathrm{0}}^{\mathrm{5}}} \\  & \mathrm{(b)0}\mathrm{.86 }\!\!\times\!\!\text{ 1}{{\mathrm{0}}^{\mathrm{4}}} \\  \end{align}\]

Ans:

Solve in exponential form

\[\begin{align} & (a)168200 \\  & (b)8600 \\  \end{align}\]

Short Answer Questions                                                          3 Marks

18. State true or false

$\begin{align} & \mathrm{(a)}\left( \mathrm{1}{{\mathrm{0}}^{\mathrm{0}}}\mathrm{+1}{{\mathrm{2}}^{\mathrm{0}}} \right)\left( \mathrm{1}{{\mathrm{6}}^{\mathrm{0}}}\mathrm{+1}{{\mathrm{2}}^{\mathrm{0}}} \right)\mathrm{}{{\mathrm{8}}^{\mathrm{2}}} \\  & \mathrm{(b)}{{\left( {{\mathrm{3}}^{\mathrm{4}}} \right)}^{\mathrm{2}}}\mathrm{=}{{\mathrm{3}}^{\mathrm{8}}} \\  & \mathrm{(c)}{{\left( {{\mathrm{5}}^{\mathrm{2}}} \right)}^{\mathrm{3}}}\mathrm{=100000} \\  \end{align}$

Ans:

(a) False

(b) True

(c) False

19. Simplify \[\dfrac{{{\mathrm{5}}^{\mathrm{2}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{a}}^{\mathrm{-4}}}}{{{\mathrm{5}}^{\mathrm{-3}}}\mathrm{ }\!\!\times\!\!\text{ 10 }\!\!\times\!\!\text{ }{{\mathrm{a}}^{\mathrm{-8}}}}\] , where \[\mathrm{a}\ne \mathrm{0}\]

Ans:

Solve the expression 

\[\begin{align} & \dfrac{{{5}^{2}}\times {{a}^{-4}}}{{{5}^{-3}}\times 10\times {{a}^{-8}}}={{5}^{2}}\times {{a}^{-4}}\times {{5}^{3}}\times 10\times {{a}^{8}} \\ & =\left( {{5}^{2}}\times {{5}^{3}} \right)\times \left( {{a}^{8}}\times {{a}^{-4}} \right)\times 10 \\  & =\left( {{5}^{2+3}} \right)\left( {{a}^{8-4}} \right)\times 10 \\  & ={{5}^{5}}\times {{a}^{4}}\times 10 \\  & \dfrac{{{5}^{2}}\times {{a}^{-4}}}{{{5}^{-3}}\times 10\times {{a}^{-8}}}=10{{(a)}^{4}}{{(5)}^{5}} \\ \end{align}\]

20. Find the area of the square attached to the hypotenuse in the diagram. Express the solution in exponential form.

(image will be uploaded soon)

Ans:

From Pythagoras theorem 

\[\begin{align} & Are{{a}_{(longside)}}={{A}_{side1}}+{{A}_{side2}} \\  & A={{5}^{2}}+{{12}^{2}} \\  & A=169 \\  & A={{13}^{2}}c{{m}^{2}} \\  \end{align}\]

21.Simplify\[\left[ \left\{ {{\left( \dfrac{\mathrm{1}}{\mathrm{3}} \right)}^{\mathrm{-3}}}\mathrm{-}{{\left( \dfrac{\mathrm{1}}{\mathrm{2}} \right)}^{\mathrm{-3}}}\mathrm{ }\!\!\div\!\!\text{ }{{\left( \dfrac{\mathrm{1}}{\mathrm{5}} \right)}^{\mathrm{-2}}} \right\} \right]\]

Ans:

Solve the expression
\[\begin{align} & \left[ \left\{ {{\left( \dfrac{1}{3} \right)}^{-3}}-{{\left( \dfrac{1}{2} \right)}^{-3}}\div {{\left( \dfrac{1}{5} \right)}^{-2}} \right\} \right] \\ & =\left[ \dfrac{{{1}^{-3}}}{{{3}^{-3}}}-\dfrac{{{1}^{-3}}}{{{2}^{-3}}}\div \dfrac{{{1}^{-2}}}{{{5}^{-2}}} \right] \\ & =\left[ \left( \dfrac{{{3}^{3}}}{{{1}^{3}}}-\dfrac{{{2}^{3}}}{{{1}^{3}}} \right)\div \dfrac{{{5}^{2}}}{{{1}^{2}}} \right] \\  & =\left( \dfrac{27}{1}-\dfrac{8}{1} \right)\div 25 \\  & =\dfrac{(27-8)}{25} \\  & =\dfrac{19}{25} \\ \end{align}\]

22. if \[\mathrm{x=}{{\left( \dfrac{\mathrm{5}}{\mathrm{2}} \right)}^{\mathrm{2}}}\mathrm{ }\!\!\times\!\!\text{ }{{\left( \dfrac{\mathrm{2}}{\mathrm{5}} \right)}^{\mathrm{-3}}}\] find the value of \[{{\mathrm{x}}^{\mathrm{-2}}}\]

Ans:

\[\begin{matrix} x={{\left( \dfrac{5}{2} \right)}^{2}}\times {{\left( \dfrac{2}{5} \right)}^{-3}}  \\ x={{\left( \dfrac{5}{2} \right)}^{2}}\times \dfrac{{{5}^{3}}}{{{2}^{3}}}  \\ x=\dfrac{{{5}^{4}}}{{{2}^{4}}}={{\left( \dfrac{5}{2} \right)}^{4}}  \\ \end{matrix}\]

The value of \[{{x}^{-2}}={{\left[ {{\left( \dfrac{5}{2} \right)}^{4}} \right]}^{-2}}\]

\[\begin{align} & {{x}^{-2}}={{\left[ {{\left( \dfrac{5}{2} \right)}^{4}} \right]}^{-2}} \\  & {{x}^{-2}}={{\left( \dfrac{5}{2} \right)}^{4\times (-2)}} \\  & {{x}^{-2}}={{\left( \dfrac{5}{2} \right)}^{-8}} \\  & {{x}^{-2}}={{\left( \dfrac{2}{5} \right)}^{8}} \\  \end{align}\]

23. Prove that \[{{\left[ {{\left( \dfrac{\mathrm{1}}{\mathrm{2}} \right)}^{\mathrm{2}}} \right]}^{\mathrm{3}}}\mathrm{ }\!\!\times\!\!\text{ }{{\left( \dfrac{\mathrm{1}}{\mathrm{3}} \right)}^{\mathrm{-4}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{-2}}}\mathrm{ }\!\!\times\!\!\text{ }\dfrac{\mathrm{1}}{\mathrm{6}}\mathrm{=}\dfrac{\mathrm{3}}{\mathrm{128}}\]

Ans:

Solve the left hand side and equate with the right

\[\begin{align} & LHS={{\left[ {{\left( \dfrac{1}{2} \right)}^{2}} \right]}^{3}}\times {{\left( \dfrac{1}{3} \right)}^{-4}}\times {{3}^{-2}}\times \dfrac{1}{6} \\  & ={{\left( \dfrac{{{1}^{2}}}{{{2}^{2}}} \right)}^{3}}\times {{\left( {{3}^{-1}} \right)}^{-4}}\times {{3}^{-2}}\times \dfrac{1}{2}\times \dfrac{1}{3} \\ & =\dfrac{1}{{{2}^{6}}}\times {{3}^{4}}\times {{3}^{-2}}\times \dfrac{1}{2}\times {{3}^{-1}} \\  & =\dfrac{1}{{{2}^{7}}}\times {{3}^{4-3}} \\  & =\dfrac{3}{128} \\  \end{align}\]

24. A dish holds \[\mathbf{100}\] bacteria. It is known that the bacteria double in number every hour.

How many bacteria will be present after each number of hours?

\[\begin{align} & \mathrm{(a)1} \\  & \mathrm{(b)5} \\  & \mathrm{(c)n} \\  & \mathrm{(d)}\dfrac{\mathrm{3}}{\mathrm{2}} \\  \end{align}\]

Ans:

Number of hours will multiply with the number of bacteria two the power of two 

\[\begin{align} & (a)100\left( {{2}^{1}} \right)=200 \\  & (b)100\left( {{2}^{5}} \right)=100\left( 32 \right) \\  & 100\left( {{2}^{5}} \right)=3200 \\  & (c)100\left( {{2}^{n}} \right) \\  & (d)100\left( {{2}^{\dfrac{3}{2}}} \right) \\ \end{align}\]

25. What is the area of the rectangle with the width of \[\mathrm{6}{{\mathrm{x}}^{\mathrm{2}}}\]and the length of\[\mathrm{12}{{\mathrm{x}}^{\mathrm{3}}}\]? After finding the area, find the solution at \[\mathrm{x=2m}\] .

Ans:

\[Area\text{ }of\text{ }rectangle\text{ }=\text{ }length\times ~breadth\]

\[\begin{align} & A=12{{x}^{3}}\times 6{{x}^{2}} \\  & A=72{{x}^{5}} \\  & at,x=2m \\  & A=72\times {{\left( 2 \right)}^{5}} \\  & A=72\times 32 \\  & A=2304{{m}^{2}} \\  \end{align}\]

Class 8 Maths Exponents and Powers Important Questions

The Exponents and Powers Class 8 Important Questions are also available in the PDF format which students can download on their devices and access offline as per their convenient time. With these questions in hand, students will surely get a better conceptual understanding and learn how to divide their time into more important topics than the less significant ones. The questions are based on the topics that are outlined below.

Topics Included in the Class 8 Maths Chapter 12 Exponents and Powers

Here is the list of topics covered in Chapter 12 Exponents and Powers.

Now let us discuss each topic in detail.

Topics in Class 8 Maths Chapter 12 Exponents and Powers

Exponents and Powers are fundamental concepts of Mathematics and are used to express very small or very large numbers in their standard forms. Some of the common terms used in this topic are:

• Power - The power of a number is expressed as xy, and it indicates how many times the number x has to be multiplied (which is y times in this example). In this expression “x” is called the base and “y” is called the exponent.

• Example of Power - 108, here the base is 10, and the exponent is 8. It is called as 10 raised to the power 8 and its value is given by multiplying 10 to itself 8 times i.e. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 100000000.

• Negative Exponents - There could be a power that has a negative exponent. These negative exponents can be converted into positive ones by the following method:

1. 8^-3 = (1/8³), so we can say that for any non-negative integer x, x^-m = 1/x^m

• Laws of Exponents:

1. Multiplication of Powers That has the Same Base - If x is a non-zero integer then x^a * x^b = x^a+b, where a and b are integers. For example 2³ * 2⁴ = 2³⁺⁴ = 27.

2. Power of Power - If x is a non-zero integer then (x^m)ⁿ = x^mn, where m and n are integers. For example (2³)⁴ = 2^3*4 = 2¹².

3. Multiplication of Powers That have Different Bases but the Same Exponent - If x and y are two non-zero integers then x^a * y^a = (x * y)^a, where a is an integer. For example 2² * 3² = (2 * 3)² = 6² = 36.

4. Division of Powers with the Same Base but Different Exponents - For a non-zero integer x, x^a/x^b = x^a-b, where a and b are integers and a > b.

5. Any number raised to the power 0 is equal to 1, i.e. x⁰ = 1, where x is any non-zero integer.

6. Any non-zero integer raised to the power 1 is equal to the same integer, i.e. x¹ = x.

7. 1/xⁿ = x^-n

List of Formulas of Class 8 Maths Chapter 12 Exponents and Powers

Find here the list of all important formulas discussed in the chapter. Students can solve all the questions asked in the chapter using the formulas given below. 

Practice Questions of Chapter 12 Exponents and Powers

For more practice, we have provided some practise questions for the students. Try to solve these questions.

1. What is the value of 90?

2. What is the value of 143/53?

3. Find the value of 75 x 95.

4. Find the value of (62)3.

5. Evaluate the value of 87 x 85.

These questions are very beneficial for the students. Practice the important questions along with the practice question given above. These questions are solved by the subject-matter experts following the pattern of CBSE guidelines.

Why are Important Questions for Class  8 Maths Chapter 12 - Exponents and Powers necessary?

• Important questions in Vedantu's Class 8 Maths Chapter 12 - Exponents and Powers help reinforce key concepts covered in the chapter.

• They serve as a targeted study resource for students preparing for exams, as they often focus on the types of questions commonly found in examinations.

• These questions are designed to challenge students' problem-solving skills, promoting a deeper understanding of the topic.

• Students can use these questions to self-assess their understanding of the chapter, identifying areas that may need further review.

• By practicing important questions, students can improve their time management skills, essential for completing exams within the allocated time.

• These questions often involve the application of theoretical knowledge to practical problems, enhancing the student's ability to apply concepts in different scenarios.

• Regular practice with important questions can boost a student's confidence, helping them approach exams with a more positive mindset.

• Important questions typically cover a range of topics within the chapter, ensuring a comprehensive review of the material.

• For students aspiring to pursue further studies or competitive exams, practicing these questions can be valuable in building a strong foundation in mathematics.

Conclusion

For CBSE Class 8 Maths Chapter 12 on Exponents and Powers, it's crucial to focus on certain key questions provided by Vedantu. These questions help understanding and mastery of the chapter. One particularly important section is likely to be emphasized, which could be related to fundamental concepts or common challenges students face in this topic. By practicing these essential questions, students can strengthen their grasp of exponents and powers, paving the way for better performance in exams and a clearer understanding of mathematical principles. Mastery of this chapter is foundational for future math learning, making these questions valuable for students.