Class 8 Maths - Exponents and Powers CBSE Worksheets Solutions

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: 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: 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

Q6: Express 512 as a power of 2.
(a) 2⁷
(b) 2⁸
(c) 2⁹
(d) 2¹⁰
Ans: (c)

Since 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹. 

Hence, option (c) is correct.

Q7: Which is the correct expression for 625?
(a) 5³
(b) 4⁵
(c) 5⁴
(d) None of these
Ans: (c)

We have 625 = 5 × 5× 5 × 5 = 5⁴.

Q8: From 2⁷, 4², 3² and  6³,  which is greater than others?
(a) 2⁷
(b) 3²
(c) 4³
(d) 6³
Ans: (d)

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. 

State true or false

Q1:  (10⁰+12⁰)(16⁰+12⁰)=8²
Ans: False

(Anything)⁰ =1  therefore, LHS= 1 

RHS= 8² = 64 

hence false 

Q2: (3⁴)²=3⁸
Ans: True

LHS= (3⁴)² = (3)⁸

^{RHS=  (3)8}

Q3: (5²)³=100000
Ans: False

LHS= (5²)³= (5)⁶ = 1000000  Hence false

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) 650200000000
(b) 301000000
Ans: Solve in exponential form
(a)650200000000=6.502×10¹¹
(b)301000000=3.01×10⁸

Q9: Express the following in expanded form
(a) 1.682 × 10⁵
(b) 0.86 × 10⁴
Ans: Solve in exponential form
(a) 168200
(b) 8600
Q10: Prove that
Ans: Solve the left hand side and equate with the right