How to Solve Exponents with Negative or Fractional Bases?
FAQs on Practice Exponents with Fractional and Negative Bases – Class 6 Worksheet
1. How do you solve exponents when the base is a negative number?
To solve an exponent with a negative base, you multiply the base by itself the number of times indicated by the exponent, paying close attention to the sign. The final sign depends on whether the exponent is even or odd.
- If the exponent is an even number (like 2, 4, 6), the result will always be positive. For example, (-3)² = (-3) × (-3) = 9.
- If the exponent is an odd number (like 1, 3, 5), the result will always be negative. For example, (-2)³ = (-2) × (-2) × (-2) = -8.
2. How do you find the value of an exponent with a fractional base?
To find the value of an exponent with a fractional base, you must raise both the numerator and the denominator to that power separately. This is a key part of the exponent rules taught in Class 6 Maths.
- The general rule is (a/b)ⁿ = aⁿ / bⁿ.
- For example, to evaluate the expression (2/3)³, you calculate 2³ and 3³ separately.
- This gives you 2³ = 8 and 3³ = 27.
- So, the final answer is 8/27.
3. Is this worksheet on exponents for Class 6 aligned with the CBSE and NCERT syllabus?
Yes, this worksheet is designed to align perfectly with the CBSE and NCERT curriculum for Class 6 Maths. It focuses on core concepts like evaluating exponents with negative bases and fractional bases, which are essential for building a strong foundation in powers and exponents. The problems provide excellent practice for school exams.
4. Does this exponents worksheet include an answer key?
Absolutely. This free printable Class 6 Maths exponents worksheet comes with a complete answer key. The solutions are provided with stepwise explanations to help students understand the correct method for solving problems and to allow parents to easily check the work for homework or revision.
5. What is the main difference between (-5)² and -5²?
The main difference between (-5)² and -5² lies in the order of operations and what the exponent applies to. This is a common point of confusion in simplifying exponents.
- In (-5)², the parentheses indicate that the base is -5. You multiply the entire base by itself: (-5) × (-5) = 25.
- In -5², there are no parentheses, so the exponent 2 applies only to the 5. You calculate 5² first (which is 25) and then apply the negative sign. The result is -25.
6. How can this Class 6 exponents worksheet help with my homework?
This worksheet is an excellent resource for homework, revision, and extra practice on exponents with fractional and negative bases. It helps by:
- Providing a variety of problems to reinforce exponent rules.
- Offering clear examples to build confidence before exams.
- Helping you identify and correct common mistakes using the included worksheet with answers.
- Improving your calculation speed and accuracy for NCERT exponent questions.
7. Is this worksheet on Class 6 Maths exponents printable?
Yes, this is a print-friendly worksheet on exponents for Class 6 available as a free downloadable PDF. You can easily print it for use in the classroom or for at-home practice, making it a convenient tool for students, parents, and teachers looking for quality educational material.
8. What is a simple rule for determining the sign of an answer when the base is negative?
The simplest rule for determining the sign of an exponential expression with a negative base depends on whether the exponent is an even or an odd number.
- Even Exponent: The result is always positive. Example: (-10)⁴ = 10,000.
- Odd Exponent: The result is always negative. Example: (-10)³ = -1000.
This is a fundamental property of exponents covered in the CBSE Class 6 exponents chapter.
9. What skills are built by solving problems on exponents with negative and fractional bases?
Solving problems from this exponents worksheet PDF helps Class 6 students build several essential mathematical skills. This maths revision activity strengthens:
- Understanding of properties of exponents and power laws.
- Proficiency in integer and fraction multiplication.
- Attention to detail, especially with negative signs and parentheses.
- Problem-solving abilities by applying exponent rules to different types of numbers.
10. What is 3 to the power of negative 2 as a fraction?
The expression 3 to the power of negative 2, written as 3⁻², is equal to the fraction 1/9. While negative exponents are often detailed in higher grades, understanding the concept is useful.
- A negative exponent means you should take the reciprocal of the base raised to the positive exponent.
- First, find the reciprocal of the base: 1/3.
- Then, apply the positive exponent: (1/3)².
- This equals (1/3) × (1/3) = 1/9.
