Power Play — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Power Play" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Power Play" — 8 important questions with detailed answers for CBSE board exam prepa…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 8 Mathematics — Power Play. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Power Play — All 8 Questions Solved
Q1. Simplify: 2⁵ × 2³
We need to multiply two powers with the same base.
Step 1: Use the law of exponents: aᵐ × aⁿ = aᵐ⁺ⁿ
Step 2: Apply the rule
2⁵ × 2³ = 2⁽⁵⁺³⁾ = 2⁸
Step 3: Calculate 2⁸
2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
Answer: 2⁵ × 2³ = 2⁸ = 256
Q2. Express 3⁻² in the form 1/aⁿ.
We need to convert a negative exponent to a positive form.
Step 1: Use the law of exponents: a⁻ⁿ = 1/aⁿ
Step 2: Apply the rule
3⁻² = 1/3²
Step 3: Calculate 3²
3² = 3 × 3 = 9
Step 4: Final answer
3⁻² = 1/9
Answer: 3⁻² = 1/9
Q3. Simplify: (5⁴/5²)
We need to divide two powers with the same base.
Step 1: Use the law of exponents: aᵐ/aⁿ = aᵐ⁻ⁿ (where m > n)
Step 2: Apply the rule
5⁴/5² = 5⁽⁴⁻²⁾ = 5²
Step 3: Calculate 5²
5² = 5 × 5 = 25
Answer: 5⁴/5² = 5² = 25
Q4. Write 0.00001 in standard form (scientific notation).
We need to express 0.00001 as a number between 1 and 10 multiplied by a power of 10.
Step 1: Identify the non-zero digits
0.00001 has the digit 1
Step 2: Place the decimal point after the first non-zero digit
1.0
Step 3: Count how many places the decimal point moved
Original: 0.00001
New position: 1.0
The decimal moved 5 places to the right.
Step 4: When moving right, use negative exponent
0.00001 = 1 × 10⁻⁵
Step 5: Verify
1 × 10⁻⁵ = 1 × (1/100000) = 1/100000 = 0.00001 ✓
Answer: 0.00001 = 1 × 10⁻⁵
Q5. Simplify: (2³)² using the law of exponents.
We need to simplify a power raised to another power.
Step 1: Use the law of exponents: (aᵐ)ⁿ = aᵐ×ⁿ
Step 2: Apply the rule
(2³)² = 2³×² = 2⁶
Step 3: Calculate 2⁶
2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
Step 4: Verify by calculating (2³)² directly
(2³)² = (8)² = 8 × 8 = 64 ✓
Answer: (2³)² = 2⁶ = 64
Q6. Write 725000 in standard form.
We need to express 725000 as a number between 1 and 10 multiplied by a power of 10.
Step 1: Identify where to place the decimal
725000 can be written as 725000.0
Step 2: Place the decimal after the first digit
7.25000
Step 3: Count how many places the decimal moved
Original: 725000.0 (decimal at the end)
New position: 7.25000
The decimal moved 5 places to the left.
Step 4: When moving left, use positive exponent
725000 = 7.25 × 10⁵
Step 5: Verify
7.25 × 10⁵ = 7.25 × 100000 = 725000 ✓
Answer: 725000 = 7.25 × 10⁵
Q7. Evaluate: (-3)⁴
We need to find the value of a negative number raised to an even power.
Step 1: Expand (-3)⁴
(-3)⁴ = (-3) × (-3) × (-3) × (-3)
Step 2: Multiply step by step
(-3) × (-3) = 9 (negative × negative = positive)
9 × (-3) = -27 (positive × negative = negative)
-27 × (-3) = 81 (negative × negative = positive)
Step 3: Verify the pattern
When a negative number is raised to an even power, the result is positive.
(-3)⁴ = 3⁴ = 81
Answer: (-3)⁴ = 81
Q8. Express 4/5 × 4/5 × 4/5 using exponents.
We need to write a repeated multiplication of fractions using exponent notation.
Step 1: Identify what is being multiplied
4/5 is multiplied three times
Step 2: Use exponent notation
4/5 × 4/5 × 4/5 = (4/5)³
Step 3: Apply the rule (a/b)ⁿ = aⁿ/bⁿ
(4/5)³ = 4³/5³
Step 4: Calculate
4³ = 4 × 4 × 4 = 64
5³ = 5 × 5 × 5 = 125
Step 5: Final answer
(4/5)³ = 64/125
Answer: 4/5 × 4/5 × 4/5 = (4/5)³ = 64/125
Power Play — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. Simplify: 5^3 × 5^2
- A. 5^6
- B. 5^1
- C. 25^5
- D. 5^5
Answer: D. 5^5 — According to the law of exponents, when multiplying powers with the same base, we add the exponents. So, 5^3 × 5^2 = 5^(3+2) = 5^5.
MCQ 2. What is the value of (2023)^0?
- A. 0
- B. 1
- C. 2023
- D. Undefined
Answer: B. 1 — Any non-zero number raised to the power of zero is equal to 1. Therefore, (2023)^0 = 1.
MCQ 3. Express 3^-2 as a positive exponent.
- A. 1/3^2
- B. -3^2
- C. 3^2
- D. 1/9
Answer: A. 1/3^2 — A negative exponent indicates the reciprocal of the base raised to the positive exponent. So, 3^-2 = 1/(3^2).
MCQ 4. Simplify: (7^8) ÷ (7^5)
- A. 7^13
- B. 7^3
- C. 7^40
- D. 1^3
Answer: B. 7^3 — According to the law of exponents, when dividing powers with the same base, we subtract the exponents. So, 7^8 ÷ 7^5 = 7^(8-5) = 7^3.
MCQ 5. What is the value of ( (2^3)^2 )?
- A. 2^5
- B. 2^6
- C. 4^6
- D. 2^9
Answer: B. 2^6 — According to the law of exponents, (a^m)^n = a^(m*n). So, (2^3)^2 = 2^(3*2) = 2^6.
MCQ 6. Express 12,300,000,000 in standard form.
- A. 1.23 × 10^10
- B. 12.3 × 10^9
- C. 1.23 × 10^11
- D. 123 × 10^8
Answer: A. 1.23 × 10^10 — To express a number in standard form, we write it as a number between 1 and 10 multiplied by a power of 10. We move the decimal point 10 places to the left, so it becomes 1.23 × 10^10.
MCQ 7. Express 0.0000000056 in standard form.
- A. 5.6 × 10^-8
- B. 5.6 × 10^-9
- C. 56 × 10^-10
- D. 0.56 × 10^-8
Answer: B. 5.6 × 10^-9 — To express a very small number in standard form, we move the decimal point to the right until there is one non-zero digit before it. We moved it 9 places, so it's 5.6 × 10^-9.
MCQ 8. Simplify: (2^5 × 2^3) ÷ 2^6
- A. 2^2
- B. 2^8
- C. 2^14
- D. 2^0
Answer: A. 2^2 — First, apply the product rule: 2^5 × 2^3 = 2^(5+3) = 2^8. Then, apply the division rule: 2^8 ÷ 2^6 = 2^(8-6) = 2^2.
MCQ 9. If 3^x = 243, what is the value of x?
- A. 3
- B. 4
- C. 5
- D. 6
Answer: C. 5 — We need to express 243 as a power of 3. 3^1=3, 3^2=9, 3^3=27, 3^4=81, 3^5=243. So, x = 5.
MCQ 10. Evaluate (-2)^-3
- A. 1/8
- B. -1/8
- C. 8
- D. -8
Answer: B. -1/8 — (-2)^-3 = 1/((-2)^3) = 1/(-8) = -1/8.
MCQ 11. What is the reciprocal of (3/4)^-2?
- A. (4/3)^2
- B. (3/4)^2
- C. (4/3)^-2
- D. -(3/4)^2
Answer: B. (3/4)^2 — The expression (3/4)^-2 is equivalent to (4/3)^2. The reciprocal of a number is 1 divided by that number. So, the reciprocal of (4/3)^2 is 1/((4/3)^2) = (3/4)^2.
MCQ 12. Simplify: ( (a^2)^3 × a^4 ) / a^7
- A. a^3
- B. a^2
- C. a^4
- D. a^1
Answer: A. a^3 — First, (a^2)^3 = a^(2*3) = a^6. Then, a^6 × a^4 = a^(6+4) = a^10. Finally, a^10 / a^7 = a^(10-7) = a^3.
MCQ 13. Which of the following is the largest? 2^10, 3^7, 4^5, 5^4
- A. 2^10
- B. 3^7
- C. 4^5
- D. 5^4
Answer: B. 3^7 — Calculate each value: 2^10 = 1024. 3^7 = 2187. 4^5 = (2^2)^5 = 2^10 = 1024. 5^4 = 625. The largest is 3^7.
MCQ 14. Simplify: (2^3 × 3^3)
- A. 6^3
- B. 6^6
- C. 5^3
- D. 2^9
Answer: A. 6^3 — According to the law of exponents, (a^m × b^m) = (a × b)^m. So, 2^3 × 3^3 = (2 × 3)^3 = 6^3.
MCQ 15. If 4^x = (1/64), what is the value of x?
- A. -3
- B. 3
- C. -2
- D. 2
Answer: A. -3 — We need to express (1/64) as a power of 4. We know that 64 = 4^3. Therefore, 1/64 = 1/(4^3) = 4^-3. So, x = -3.
MCQ 16. Evaluate: (1/5)^-1
- A. 5
- B. 1/5
- C. -5
- D. -1/5
Answer: A. 5 — A base raised to the power of -1 is its reciprocal. So, (1/5)^-1 = 5.
MCQ 17. What is the value of (2/3)^-2?
- A. 9/4
- B. 4/9
- C. -4/9
- D. -9/4
Answer: A. 9/4 — To evaluate (2/3)^-2, we take the reciprocal of the base and change the sign of the exponent. So, (2/3)^-2 = (3/2)^2 = (3^2)/(2^2) = 9/4.
MCQ 18. The speed of light is approximately 3 × 10^8 meters per second. If it takes light 500 seconds to travel from the Sun to Earth, what is the approximate distance in meters?
- A. 1.5 × 10^11
- B. 1.5 × 10^10
- C. 15 × 10^10
- D. 3 × 10^8
Answer: A. 1.5 × 10^11 — Distance = Speed × Time. Distance = (3 × 10^8) × 500 = (3 × 10^8) × (5 × 10^2) = 15 × 10^(8+2) = 15 × 10^10. In standard form, this is 1.5 × 10^11 meters.
MCQ 19. In the expression 7^5, what is the base and what is the exponent?
- A. Base=7, Exponent=5
- B. Base=5, Exponent=7
- C. Base=7, Exponent=-5
- D. Base=1/7, Exponent=5
Answer: A. Base=7, Exponent=5 — In an exponential expression a^b, 'a' is the base and 'b' is the exponent (or power). So, 7 is the base and 5 is the exponent.
MCQ 20. Simplify: (-3)^4 × 3^2
- A. 3^6
- B. -3^6
- C. 9^6
- D. (-3)^8
Answer: A. 3^6 — Since the exponent is even, (-3)^4 is positive, so (-3)^4 = 3^4. Then, 3^4 × 3^2 = 3^(4+2) = 3^6.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.