Exponents and Powers Class 8 MCQ

Answer: (a) 66/13

Explanation: 13⁻¹+12⁰+2²

Applying a^-n=1/aⁿ ( where a ≠ 0 ) for 13⁻¹

= (1/13) + 12⁰ + 2²

= (1/13) + 1 + 4 Applying [ a⁰ = 1 ] for we would get 12⁰ = 1

= (1/13) + 5

= (1+65)/13

= 66/13

Answer: (b) -5

Explanation: Given

7²⁰÷7⁸=7⁻⁷÷7³ⁿ⁻⁴

Or7²⁰⁻⁸ = 7^−7−3n+4       Since a^m÷ aⁿ=a^m−n( a ≠ 0 )

7¹²=7⁻³⁻³ⁿ

On comparing the index\exponent of the two sides (Since the base is equal to 7 )

We get,

12 = -3 – 3 n

12 + 3 = – 3 n

15 = – 3 n

15/3 = – n

n = -5

Answer: (A) Two

Explanation: We know that

a^m÷ aⁿ=a^m−n( a ≠ 0 )

Given =13⁷÷13¹

Applying

a^m÷ aⁿ=a^m−n( a ≠ 0 )

=[13^7-1]

= 13⁶

Answer: (b) 144

Explanation: In such a question, where both the numbers are different, we simply break them down into the individual multiples

= 3²×(−4)²

Writing individual multiples of 3²×(−4)²

= 3 x 3 x -4 x -4

= 9 x 16

= 144

Answer: (c) 10/33

Explanation: Given (3(3/10))^-1 = (33/10)^-1

We know that ( (a/b)^-n= (b/a)ⁿ

Comparing (ab)^-n to the given equation, we would get a = 33 , b = 10 and n = – 1

(b/a)ⁿ

We would get

= (10/33)¹

= 10/33

Answer: (c) 86

Explanation: (1/6)⁰ + (1/4)^-1 + (1/9)^-2

Applying (a⁰ = 1 ) to (1/6)⁰ and Applying ( a^-n = (1/aⁿ) to (1/4)^-1 and (1/9)^-2

We would get

= 1 + (4/1)¹ + (9/1)²

= 1 + 4 + 81

= 86

Answer: (b) 4

Explanation: (√25 – √9)^1/2(√25 + √9)^1/2

The above equation can be written as (a-b)(a +b)

Where a =√25 and b = √9

We know that (a−b)(a +b)=a²−b² ,

Applying (a−b)(a+ b)=a²−b²

[(√25)² – (√9)²]^1/2

[25−9]^1/2

[16]^1/2

Since 16 = ( 4² ) , we can write the given equation as

(4²)^1/2

=4^2×(1/2)

= 4¹

= 4

Answer: (a) 343

Explanation: 7¹⁴ × 7⁴/(7⁵)³

= 7¹⁴ × 7⁴/(7¹⁵) Substituting(7⁵)³with715 as(a^m)ⁿ = a^mn

= 7¹⁴⁺⁴/(7¹⁵)

= (7¹⁸)/(7¹⁵)

=7¹⁸⁻¹⁵ Since a^m=a^m−n

=7³

= 343

Answer: (b) 12⁶⁰

Explanation: We know that (a^m)ⁿ=a^mn

If we solve {(12)³}²

(12)^3×2 =12⁶

Adding this value to the given equation

= (12⁶)¹⁰

= 12^6×10

= 12⁶⁰

Hence, the answer is 12⁶⁰

Answer: (c) 64a⁶b^-23

Explanation: (-2a^7/6b^-23/6)⁶

(−2)⁶ x (a^7/6)⁶x (b^-23/6)⁶ (a^m)ⁿ=a^mn ]

= 64 xa^(7/6)×6 x b^(−23/6)×6

= 64 x a⁷ x b⁻²³

=64a⁷b⁻²³

Answer: (a) a^-28 × a^-20

Explanation: (a^-7b^-5)⁴

It can be written as

(a^-7)⁴ x (b^-5)⁴            [(a ^p b ^q)^r=(a ^p)^r×(b ^q)^r ]

= a^−7×4 x b^−5×4

= a⁻²⁸ x b⁻²⁰

Answer: (a) (5/2)³

Explanation: (2/5)^-3

Applying (a⁻ⁿ=1/aⁿ ) we would get

(2/5)^-3 = (5/2)³

Reciprocal of (2/5)^-3 is (5/2)³

Answer: (b) 257/16

Explanation: We need to find the value of a^b + b^a

Given a = 2 , b = -4

If we substitute these value in the given equation, we would get

= 2^-4 + −4²

= (1/2⁴) + −4² ( since 1/a^m=a^-m )

= (1/16)+ 16

= (1+256)/16

= 257/16

Answer: (c) 17/12

Explanation: √m/n = (n/m)^8-6x

(m/n)^1/2 = (n/m)^8-6x

We know that (a/b)ⁿ = (b/a)⁻ⁿ

Applying this, we can say that (m/n)^1/2 =(n/m)^−1/2

(n/m)^−1/2 = (n/m)^8-6x

Since the base of both the numbers is the same, the index values should also be equal, i.e,

−1/2 = 8 – 6 x

-1 = 2 ( 8 – 6 x )

-1 = 16 – 12 x

12 x = 16 + 1

x = 17/12

Answer: (a) -13/6

Explanation: Given 13^6y+13 =1

We know that 1 = 13⁰

If we substitute these values in the given equation, we would get

13^6y+13 = 13⁰ Since [ 1 = 13⁰ ]

Since the base of both the numbers is the same, the index values should also be equal, i.e.,

6 y + 13 = 0

6 y = -13

y = −13/6

Answer: (a) 2

Explanation: 5ⁿ = √15625 ÷ (5⁶)^1/6

In order to find the value of n, we would need to make the right hand side to such a value, that the base of the given value is equal to 5

5ⁿ = √5⁶ ÷ (5^6×(1/6))

5ⁿ = (5⁶)^1/2 ÷ ( 5¹ )

5ⁿ = (5^6×(1/2)) ÷ (5¹)                Since (a^m)ⁿ= a ^mn

5ⁿ = 5³ ÷5¹

5ⁿ = 5³⁻¹           Since [a ^m aⁿ]=a^m−n

5ⁿ = 5²

Comparing the power of both the sides(since the index is common)

n = 2

Answer: (a) 16

Explanation: (64)^2/3

64 can be written as 4 x 4 x 4

Or (4)³

=(4³)^2/3

Using the equation

(a^m)ⁿ=a ^{m n}

We can rewrite the given equation as

=4^3×(2/3)

= 4²

= 16

Answer: (a) 32p^-5

Explanation: (128p^-6)^5/6

= ( 2⁶p^-6 ) ( 128 = 2 x 2 x 2 x 2 x 2 x 2)

= (2⁶)^5/6 (p^-6)^5/6

= 2⁶×^5/6  p^-6×^5/6                (a^m)ⁿ=a ^{m n}

= 2⁵p^-5

= 32 p^-5

Answer: (a) 5x⁴y⁶

Explanation: 5x⁹y⁴/x⁵y^-2

=5x⁹⁻⁵y⁴⁺² [a^m aⁿ=a^m−n]

= 5x⁴y⁶