Class 8 Revision Notes CBSE Maths Chapter 12 Exponents and Powers [Free PDF Download]

The following exponent laws apply to numbers with exponents.

1. ${{\text{a}}^{\text{m}}}\text{ }\times \text{ }{{\text{a}}^{\text{n }}}\text{= }{{\text{a}}^{\text{m+n}}}$

2. ${{\text{a}}^{\text{m}}}\text{ }\div \text{ }{{\text{a}}^{\text{n }}}\text{= }{{\text{a}}^{\text{m-n}}}$

3. ${{\left( {{\text{a}}^{\text{m}}} \right)}^{\text{n}}}\text{ = }{{\text{a}}^{\text{mn}}}$

4. ${{\text{a}}^{\text{m}}}\text{ }\times \text{ }{{\text{b}}^{\text{m }}}\text{= }{{\left( \text{ab} \right)}^{\text{m}}}$

5. ${{\text{a}}^{\text{0}}}\text{ = 1}$

6. $\frac{{{\text{a}}^{\text{m}}}}{{{\text{b}}^{\text{m}}}}\text{ = }{{\left( \frac{\text{a}}{\text{b}} \right)}^{\text{m}}}$

• Negative exponents can be used to express very tiny values in standard form. Exponents are used to express small numbers in standard form as follows:

• Standard form can be used to express both very big and very small numbers.

• Scientific notation form is another name for standard form.

• If m is a decimal number, where $\text{1 }\le \text{ m  10}$ and n is either a positive or negative integer, then a number represented as $\text{m }\times \text{ 1}{{\text{0}}^{\text{n}}}$ is said to be in standard form, \[150,000,000,000\text{ }=\text{ }1.5\text{ }\times \text{ }{{10}^{11}}\], for example.

• The use of exponential notation to indicate repeated multiplication of the same number is very useful. The product \[\text{a  }\!\!\times\!\!\text{  a  }\!\!\times\!\!\text{  a  }\!\!\times\!\!\text{  a  }\!\!\times\!\!\text{  a}...\text{  }\!\!\times\!\!\text{  a (n times) = }{{\text{a}}^{\text{n}}}\], for any non-zero rational integer ‘a' and a natural number n.

• It is written as ‘a' raised to the power ‘n' and is referred to as the nth power of ‘a.' The base is the rational number a, and the exponent is the rational number n.