Class 8 Maths · Original EZT practice
Power Play (Class 8 Chapter 2): summary and practice
A power packs repeated multiplication into one compact symbol. This chapter builds exponential notation, works through the laws of exponents with positive and negative bases, uses powers of 10 to tame very large and very small numbers, and ends with a pinch of history. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. Exponential notation
n repeated factors of a are written a^n - the base a, the exponent n. So 10^6 is a lakh squared: a million. The same number has many forms: 64 = 2^6 = 4^3 = 8^2.
2. Laws of exponents
Same base: add exponents to multiply (a^m x a^n = a^(m+n)), subtract to divide, and (a^m)^n = a^(mn). Same exponent: a^m x b^m = (ab)^m. And a^0 = 1 for every non-zero a.
3. Powers of 1, 0 and negative bases
1 to any power is 1 and 0 to any power is 0. With a negative base, even powers give positive answers and odd powers negative - so (-1)^56 = 1 and (-1)^87 = -1.
4. Powers of 10, base conversion and history
Powers of 10 make huge numbers readable: 10^3 is a thousand, 10^7 a crore, 10^24 a septrillion. Any base converts the same way - 2^7 = 2^2 x 2^5 = 4 x 32 = 128. Modern notation grew from Rene Descartes's 1637 superscripts.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
One number, many powers
Choose the method: Look for repeated multiplication inside the number.
EZT practice question
Write 64 as a power in as many ways as you can.
Show the worked solution
- 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2^6.
- Pair them up: 64 = 4 x 4 x 4 = 4^3.
- Or bigger steps: 64 = 8 x 8 = 8^2.
Answer: 64 = 2^6 = 4^3 = 8^2.
Check: Each version multiplies out to 64 - and the exponents 6, 3, 2 are exactly the factorisations of 6.
Watch for this: The base must be multiplied by itself - 2^6 is not 2 x 6.
Now try it yourself
Write 81 as a power in two ways.
Check your answer
9^2 and 3^4.
9 x 9 = 81 and 3 x 3 x 3 x 3 = 81.
Multiply same-base powers
Choose the method: Keep the base, add the exponents.
EZT practice question
Compute 3^2 x 3^5 as a single power.
Show the worked solution
- 3^2 x 3^5 = 3^(2+5) = 3^7.
- Because we are multiplying 2 threes by 5 threes - 7 threes in all.
- 3^7 = 2187.
Answer: 3^7 = 2187.
Check: Directly: 9 x 243 = 2187. The law a^m x a^n = a^(m+n) is just counting factors.
Watch for this: Never multiply the bases - 3^2 x 3^5 is not 9^7.
Now try it yourself
5^3 x 5^4?
Check your answer
5^7 = 78125.
3 + 4 = 7 factors of 5.
Raise a power to a power
Choose the method: Keep the base, multiply the exponents.
EZT practice question
Simplify (2^3)^4.
Show the worked solution
- (2^3)^4 = 2^3 x 2^3 x 2^3 x 2^3.
- That is 3 + 3 + 3 + 3 = 12 factors of 2.
- So (2^3)^4 = 2^12 = 4096.
Answer: 2^12 = 4096.
Check: Directly: 2^3 = 8 and 8^4 = 4096. The rule (a^m)^n = a^(mn) counts the same factors faster.
Watch for this: (a^m)^n multiplies exponents - it does not add them.
Now try it yourself
(10^2)^3?
Check your answer
10^6 = 1000000.
2 x 3 = 6 factors of 10.
Powers of a negative base
Choose the method: Even exponent: positive answer. Odd exponent: negative answer.
EZT practice question
Evaluate (-1)^56 and (-1)^87.
Show the worked solution
- 56 is even - an even number of -1 factors pairs up to give +1s.
- So (-1)^56 = 1.
- 87 is odd - one unpaired -1 remains, so (-1)^87 = -1.
Answer: (-1)^56 = 1 and (-1)^87 = -1.
Check: Every pair (-1) x (-1) = 1; parity alone decides the sign. The same rule gives (-2)^4 = 16 but (-2)^3 = -8.
Watch for this: (-a)^n and -a^n are different - brackets decide whether the minus sign is part of the base.
Now try it yourself
(-3)^3?
Check your answer
-27.
Odd exponent on a negative base keeps the answer negative.
Read powers of 10
Choose the method: The exponent counts the zeros after 1.
EZT practice question
Write one million as a power of 10, and 10^7 in Indian naming.
Show the worked solution
- One million = 1000000 = 10^6.
- 10^7 = 10000000 - that is one crore.
- So a crore is exactly ten million.
Answer: 1000000 = 10^6; 10^7 = 1 crore.
Check: Count the zeros: 10^6 has six, 10^7 has seven. Powers of 10 let us write googol (10^100) or a septrillion (10^24) without a page of zeros.
Watch for this: Do not count digits - 10^n has n zeros after the 1, that is n + 1 digits.
Now try it yourself
10^4?
Check your answer
10000 - ten thousand.
Four zeros after the 1.
Convert between bases
Choose the method: Split the exponent so a known power factors out.
EZT practice question
Write 2^7 using base 4.
Show the worked solution
- 2^7 = 2^2 x 2^5 (since 2 + 5 = 7).
- 2^2 = 4, and 2^5 = 32.
- So 2^7 = 4 x 32 = 128.
Answer: 2^7 = 4 x 32 = 128.
Check: Directly: 2^7 = 128, and 4 x 32 = 128. Splitting exponents is the product law run backwards.
Watch for this: When splitting, the exponents must ADD to the original - 2 + 5 = 7 here.
Now try it yourself
Write 2^9 using base 8.
Check your answer
2^9 = (2^3)^3 = 8^3 = 512.
3 x 3 = 9 factors, grouped as three 8s.
Try a mixed set
Choose a method or explanation before opening each answer.
1. a^m x a^n?
Show answer and reason
a^(m+n).
Multiplying same-base powers adds the exponents.
2. (a^m)^n?
Show answer and reason
a^(mn).
A power of a power multiplies the exponents.
3. (-1) with an even exponent?
Show answer and reason
1.
Pairs of -1 multiply to +1.
4. 10^7 in Indian naming?
Show answer and reason
One crore.
10000000 - seven zeros.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Simplify 5^4 x 5^2 / 5^3 as a single power.
- Evaluate (-2)^5.
- Express 1000000000 as a power of 10 and name it.
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Questions about this practice page
- What is the law for multiplying powers with the same base?
- Add the exponents: a^m x a^n = a^(m+n). For example, 3^2 x 3^5 = 3^7 = 2187, because we are multiplying 2 threes by 5 threes.
- Is 1^0 equal to 1?
- Yes - any non-zero number raised to the power 0 is 1, and 1 to any power is 1. So 1^0 = 1^6 = 1, while 0 to any positive power is 0.
- How do powers of negative numbers behave?
- An even power of a negative base is positive and an odd power is negative: (-2)^4 = 16 but (-2)^3 = -8. In particular (-1)^even = 1 and (-1)^odd = -1.
- Why are powers of 10 useful?
- They make very large and very small numbers compact - 10^6 is a million, 10^7 a crore, 10^24 a septrillion - and they are the backbone of scientific notation and unit prefixes.
- Are these the NCERT exercise questions for Power Play (Class 8)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.