Worksheet Solutions: Power Play | Worksheets with Solutions for Class 8 PDF Download

1. Multiple Choice Questions

Q1: What is the base of the exponent 6⁹?
(a) 6
(b) 2
(c) 9
(d) None
Ans: (a)

The base of the exponent 6⁹ is 6

Q2: Find the missing number 

(a) 2
(b) −5
(c) 1
(d) None

Ans: (b)

The missing number should be  −5
So the answer will be 7⁵ =

Q3: Find the value of  (5²)²
(a) 125
(b) 625
(c) 25
(d) 0
Ans: (b)

The solution will be
(5²)²=5⁴
(5²)²=5×5×5×5
(5²)²= 625

Q4: In prime factorization, 3600 can be written as:
(a) 2⁴ × 3² × 5²
(b) 2³ × 3³ × 5²
(c) 2⁴ × 3² × 5³
(d) 2² × 3⁴ × 5²
Answer: (a) 

3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

Q5: Find the value of x, when 2^x=4⁴
(a) x=6
(b) x=2
(c) x=8
(d) x=−5
Ans: (c)

The solution will be
2^x=4⁴
2^x=(2²)⁴
2^x=2⁸
2^x=2⁸
x=8
So the answer will be x=8

Q5: Which rule of exponents is used in the expression (3²)⁴ = 3⁸?
(a) Product Rule
(b) Power of a Power Rule
(c) Quotient Rule
(d) Negative Exponent Rule

Answer: (b)

Q6: Which of the following is the usual form of 5.8 × 10¹²?
(a) 5800000000000
(b) 580000000000
(c) 0.0000000000058
(d) 5.8 × 1000000000
Answer: (a) 5800000000000

Q7: Which of the following is the correct result of 2³ × 5³?
(a) 10³
(b) 7³
(c) 1000
(d) Both (a) and (c)
Answer: (d) 

2³ × 5³ = (2 × 5)³ = 10³ = 1000

Q8: If a password can be made using 26 letters and has 4 characters, the total number of possible passwords is:
(a) 26⁴
(b) 4²⁶
(c) 26 × 4
(d) 4²⁶²
Answer: (a)

26 choices for each of 4 positions.

Q9: The scientific notation of 9540000000000000 is:
(a) 9.54 × 10¹⁵
(b) 95.4 × 10¹⁴
(c) 0.954 × 10¹⁶
(d) 9.54 × 10¹⁴

Answer: (a) 9.54 × 10¹⁵

Q10: Find the value of (2¹¹+6²−5¹)⁰= ?
(a) 0
(b) −1
(c) 1
(d) None
Ans: (c)

The solution will be
(2¹¹+6²−5¹)⁰=(anything)⁰
(2¹¹+6²−5¹)⁰=1
So the solution will be
(2¹¹+6²−5¹)⁰=1

2. State true or false

Q1:  (10⁰+12⁰)(16⁰+12⁰)=8²
Ans: False

Sol: (Anything)⁰ =1  therefore, LHS= 1 

RHS= 8² = 64 

hence false 

Q2: (3⁴)²=3⁸
Ans: True

Sol: LHS = (3⁴)² = (3)⁸

^{RHS =  (3)8}

Q3: According to the product rule of exponents, 3² × 3⁵ = 3¹⁰.
Ans: False

Sol: It should be 3⁽²⁺⁵⁾ = 3⁷.

Q4: Among 2⁷,3²,4², and 6³, 6³ is the greatest.
Ans: True

Sol: Since we have
2⁷ = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
3² = 3 × 3 = 9
4² = 4 × 4 = 16
6³ = 6 × 6 × 6 = 216
In this, 6³ is greater. 

Q5: Linear growth means multiplying by a fixed factor at each step.
Ans: False 

Sol: The statement describes exponential growth; linear growth adds a fixed amount.

Q6: The zero exponent rule states that 0ⁿ = 1 for all values of n.
Ans: False 

Sol: The zero exponent rule applies only when the base is not zero.

3. Fill in the Blanks 

Q1: The power of a power rule states that (nᵃ)ᵇ =________.
Ans: n⁽ᵃ×ᵇ⁾

Q2: Using the quotient rule: 7⁹ ÷ 7⁴ = ________.
Ans:  7⁵

Q3: The negative exponent rule says 3⁻² = _______.
Ans:  1/9

Q4: Prime factorization of 81 in exponential form is _______.
Ans: 3⁴

Q5: A number in scientific notation is written as x × 10ᵃ where 1 ≤ x < _______.
Ans: 10

6. Answer the following Questions

Q1: Follow the pattern and complete

Ans: The pattern for the solution is square root of the numbers which continue as
1234321=1111²
123454321=11111²

Q2: If 2^x × 5^x=1000 then x=?
Ans: For solving we will just factorise
2^x ×5^x=1000
2^x × 5^x = 5 × 5 × 5 × 2 × 2 × 2
2^x × 5^x = 2³ × 5³
x = 3

Q3: Find 3³+ 4³ + 5³ and give the answers in cube
Ans: Solve the expression
3³+4³+5³ = 27+64+125
3³+4³+5³ = 216
3³+4³+5³ = 6×6×6
3³+4³+5³ = 6³

Q4: Find the missing number x in  5²+x²=13²
Ans: Solve the expression
5²+x²=13²
25+x²=169
x²=144
x=√144
x=12

Q5: Simplify in exponent form (3⁴× 3²)÷ 3⁻⁴
Ans: Solving the expression

Q6: Expand
(a) 1526.26
(b) 8379
Using exponents
Ans: Solve in exponential form
(a) 1526.26 = 1×10³+5×10²+2×10¹+6×10⁰ +2×10⁻¹ + 6×10⁻²
(b) 8379 = 8×10³+3×10²+7×10¹+9×10⁰

Q7: Express the following number as a product of powers of prime factors.
(a) 1225
(b) 3600
Ans: Solve in exponential form
(a) 1225=5×5×7×7
1225=5²×7²
(b) 3600=2×2×2×2×3×3×5×5
3600=2⁴×3²×5²

Q8: Express the following large no’s in its scientific notation.
(a) 491200000
(b) 301000000
Ans: Solve in exponential form
(a) 491200000, move the decimal point 8 places to the left: 4.912×10⁸
(b) 9540000000000000, move the decimal point 15 places to the left: 9.54 × 10¹⁵

Q9: Express the following in usual form
(a) 3.02 ×10⁻⁶
(b) 5.8 × 10¹²
Ans: (a) 3.02 ×10⁻⁶
To convert a smaller number(negative powers of 10) to its usual form shift the decimal towards the left by the number of places equivalent to the power of 10.
3.02 × 10⁻⁶ = 3.02/1000000
∴ its usual form is 0.00000302
(b) 5.8 × 10¹² = 5800000000000 [Moving the decimal towards the right by 12 places]
∴ its usual form is 5800000000000

Q10: Prove that 

Ans: Solve the left hand side and equate with the right

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