Class 8 Maths

# Exponents and Power

## Exercise 12.1

Question 1: Evaluate.

(i) 3–2

Answer: 3-2 =(1)/(3^2)=1/9

(ii) (– 4)^(– 2)

Answer: (-4)^(-2)=(1)/(-4)^2=(1)/(16)

(iii) (1/2)^(-2)+(1/3)^(-2)+(1/4)^(-2)

Answer: = 22 + 32 + 42 = 4 + 9 + 16 = 29

Question 2: Simplify and express the result in power notation with positive exponent.

(i) (-4)^5÷(-4)^8

Answer: a^m÷a^n=a^(m-n)

So, (-4)^5÷(-4)^8

=(-4)^(5-3)=(-4)^(-3)

(ii) ((1)/(2^3))^2

Answer: (a^m)^n=a^(mn)

So, ((1)/(2^3))^2

=1/(2^6)=1/(64)

(iii) -3^4xx(5/3)^4

Answer: Since power on 3 is even so -3^4=3^4

So, given expression can be written as follows:

3^4xx3^(-4)xx5^4

=3^(4-4)xx5^4

=3^0xx5^4=1xx5^4=625

(iv) (3^(-7)÷3^(-10))xx3^(-5)

Answer: 3^(-7+10-5)=3^(-2)=((1)/(3^2))

(v) 2^(-3)xx (-7)^(-3)

Answer: ((1)/(2^3))xx((1)/(-7)^3)

=((1)/(-14)^3)

Question 3: Find the value of.

(i) (3^0 + 4^(-1)) xx 2^2

Answer: (3^0 + 4^(-1)) xx 2^2

=(1+1/4)xx4=5/4xx4=5

(ii) (2^(-1) xx 4^(-1)) ÷ 2^(-2)

Answer: =(1/2xx1/4)÷1/4

=1/2xx1/4xx4=1/2

(iii) (1/2)^(-2)+(1/3)^(-2)+(1/4)^(-2)

Answer: =2^2+3^2+4^2

=4+9+16=29

(iv) (3^(-1)+4^(-1)+(5^-1)^0

Answer: We know that a^0=1

So, (3^(-1)+4^(-1)+(5^-1)^0=1

(v) [((-2)/(3))^(-2)]^2

Answer: =((3^2)/(2^2))^2

=(3^4)/(2^4)=(81)/(16)

Question 4: Evaluate

(i) (8^(-1)xx5^3)/(2^(-4))

Answer: =((2^3)^(-1)xx5^3)/(2^(-4))

=2^(-3)xx2^4xx5^3

=2^(-3+4)xx5^3=2^1xx5^3=5^3

(ii) (5^(-1)xx2^(-1))xx6^(-1)

Answer: =1/5xx1/2xx1/6=(1)/(60)

Question 5: Find the value of m for which 5^m ÷ 5^(-3) = 5^5

Answer: a^5 = a^(m-n)
Here, m-n = 5 and n = -3
So, m = 5+(-3)=2

Question 6: Evaluate

(i) ((1/3)^(-1)-(1/4)^(-1))^(-1)

Answer: =(3-4)^(-1)=-1^(-1)=-1

(ii) (5/8)^(-7)xx(8/5)^(-4)

Answer: =(8/5)^7xx(5/8)^4

=(8^7)/(8^4)xx(5^4)/(5^7)

=(8^3)/(5^3)=(512)/(125)

Question 7: Simplify.

(i) (25 xx t^(-4))/(5^(-3) xx 10 xx t^(-8))

Answer: =(25 xx t^(-4))/(5^(-3) xx 10 xx t^(-8))
=(5^2 xx t^(-4))/(5^(-3) xx 5 xx 2 xx t^(-8))
= 5^(2+2) xx t^(-4+8) ÷ 2
= 5^4 xx t^4 ÷ 2

(ii) (3^(-5) xx 10^(-5) xx 125)/(5^(-7) xx 6^(-5))

Answer: = (3^(-5) xx 5^(-5) xx 2^(-5) xx 5^3)/(5^(-7) xx 6^(-5))
= (3^(-5) xx 5^(-5+3) xx 2^(-5))/(5^(-7) xx 6^(-5))
= (3^(-5) xx 5^(-2) xx 2^(-5)) /(5^(-7) xx 3^(-5) xx 2^(-5))
= (3^(-5+5) xx 5^(-2+7) xx 2^(-5+5))
= (3^0 xx 5^5 xx 2^0)
=3125