Start with the meaning
NCERT connection: Grade 8 Ganita Prakash Part I, “Power Play”. These are independent BananaLearn notes and original practice, not official NCERT material or a complete set of textbook exercise solutions. Match the chapter name to the book used by your school. Understand multiplication, division, fractions and brackets. This page selects core exponent skills; it is not a complete chapter solution set.
Multiply powers with a common base
For positive integer exponents, aᵐ × aⁿ = aᵐ⁺ⁿ because the two products contain m + n copies of a. For example, 3² × 3⁴ has six factors of three.
The rule applies to multiplication of powers with the same base. It does not turn a sum into a power, and it does not allow adding the exponents of 2³ and 5² just because both numbers are written as powers.
Divide powers and explain zero exponents
For a nonzero base, aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Cancel equal factors from numerator and denominator. For 5⁴ ÷ 5², two factors of five remain, giving 5².
Dividing a nonzero power by itself gives one. The exponent difference is zero, so a⁰ = 1 for nonzero a. This argument does not define 0⁰; leave that expression outside the rule used here.
Read a negative exponent as a reciprocal
For nonzero a and a positive integer n, a⁻ⁿ = 1/aⁿ. Thus 2⁻³ = 1/8. The negative exponent does not mean that the value is −8.
A power raised to another positive integer power repeats the entire product: (aᵐ)ⁿ = aᵐⁿ. With (2³)², there are two groups of three factors, giving 2⁶, not 2⁵.
Check signs and standard form
Brackets decide the base. (−3)² = 9 because the base is −3. In −3², the exponent applies to 3 before the outside minus, giving −9. Write the intended brackets before calculating.
In standard scientific notation, a positive number is written c × 10ⁿ with 1 ≤ c < 10 and integer n. For 45,000 use 4.5 × 10⁴. For 0.006 use 6 × 10⁻³. Reconstruct the original number to check the exponent sign.
Worked examples, step by step
Example 1: Simplify 4² × 4³
- The operation is multiplication and both bases are four.
- Add the exponents: 4² × 4³ = 4⁵.
- Check 16 × 64 = 1,024, which is 4⁵.
Example 2: Calculate 3² ÷ 3⁴
- The base is nonzero, so subtract the exponents: 3²⁻⁴ = 3⁻².
- A negative exponent denotes the reciprocal: 3⁻² = 1/3².
- The result is 1/9; check 9 ÷ 81 = 1/9.
Example 3: Write 720,000 in standard scientific notation
- Choose a coefficient between one and ten: 7.2.
- Multiplying 7.2 by 100,000 gives 720,000.
- Since 100,000 = 10⁵, the result is 7.2 × 10⁵.
Common mistakes and useful repairs
Adding exponents in an addition problem
Evaluate 2³ + 2² as 8 + 4 = 12. The common-base multiplication rule does not apply to addition.
Moving a negative exponent into a negative value
3⁻² is 1/9. A negative base and a negative exponent mean different things; identify the base and exponent separately.
Try before revealing
Quick understanding check
Read the check answers
5⁵. Multiplication with a common base adds the exponents.
1/100. The negative exponent means a reciprocal, not a negative value.
Grade 8 Power Play: exponents, rules and practice questions — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
Evaluate 2⁵.
Show answer and reasoning
32. Multiply five factors of two.
Simplify 3² × 3³ and evaluate.
Show answer and reasoning
3⁵ = 243. There are five factors of three altogether.
Simplify 7⁴ ÷ 7² and evaluate.
Show answer and reasoning
7² = 49. Subtract exponents because the base is the same and nonzero.
Evaluate (2³)².
Show answer and reasoning
64. Multiply exponents: 2⁶ = 64.
Evaluate 5⁰.
Show answer and reasoning
1. Any nonzero base to exponent zero equals one.
Evaluate 2⁻⁴.
Show answer and reasoning
1/16. Take the reciprocal of 2⁴.
Evaluate (−4)² and −4².
Show answer and reasoning
16 and −16. The first squares the negative base; the second applies an outside minus after squaring four.
Write 0.0008 in standard scientific notation.
Show answer and reasoning
8 × 10⁻⁴. 8 × 1/10,000 = 0.0008, and eight is between one and ten.
Grade 8 Power Play: exponents, rules and practice questions — worked answer key
32. Multiply five factors of two.
3⁵ = 243. There are five factors of three altogether.
7² = 49. Subtract exponents because the base is the same and nonzero.
64. Multiply exponents: 2⁶ = 64.
1. Any nonzero base to exponent zero equals one.
1/16. Take the reciprocal of 2⁴.
16 and −16. The first squares the negative base; the second applies an outside minus after squaring four.
8 × 10⁻⁴. 8 × 1/10,000 = 0.0008, and eight is between one and ten.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to Order of operations: multiplication and division share a level before trying a fresh problem.
Help at home: Ask when a rule is allowed
Write 2² × 2³ next to 2² + 2³. Ask your child to expand each expression before simplifying. This makes the operation difference visible.
If rules are mixed up, use small powers that can be checked by direct multiplication. Ask for a numerical check after the symbolic step, then move to larger powers when the conditions are clear.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Are these NCERT exercise solutions?
No. These are original questions with worked answers that support the named topic. Use the official textbook link for the book itself. Exercise numbers and school sequences can differ between editions.
How should a parent use the practice?
Ask for one independent attempt before revealing an answer. Notice whether the difficulty is reading the question, representing the idea or calculating. Revisit the matching example, then try a fresh question rather than copying the worked answer.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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