Class 9 Maths

# Number System

## Exercise 1.6

Important Laws on Indices:

• a^m.a^n=a^(m+n)
• (a^m)^n=a^(mn)
• (a^m)/(a^n)=a^(m-n)
• a^m\b^m=(ab)^m

Question 1: Find

(i) 64^(1/2)

Answer: Given, 64^(1/2)

=(8xx8)^(1/2)=(8^2)^(1/2)

=8^(2xx1/2)=8^1=8

(ii) 32^(1/5)

Answer: Given, 32^(1/5)

=(2xx2xx2xx2xx2)^(1/5)

=2^(5xx1/5)=2^1=2

(iii) 125^(1/3)

Answer: Given, 125^(1/3)

=(5xx5xx5)^(1/3)

=(5^3)^(1/3)=5^1=5

Question 2: Find

(i) 9^(3/2)

Answer: Given, 9^(3/2)

=(3^2)^(3/2)

=3^(2xx3/2)=3^3=27

(ii) 32^(2/5)

Answer: Given, 32^(2/5)

=(2xx2xx2xx2xx2)^(2/5)

=(2^5)^(2/5)=2^(5xx2/5)=2^2=4

(iii) 16^(3/4)

Answer: Given, 16^(3/4)

=(2xx2xx2xx2)^(3/4)

=(2^4)^(3/4)=2^(4xx3/4)=2^3=8

(iv) 125^(-1/3)

Answer: Given, 125^(-1/3)

=(5xx5xx5)^(-1/3)

=(5^3)^(-1/3)=5^(3xx-1/3)=5^-1=1/5

Question 3: Simplify

(i) 2^(2/3).2^(1/5)

Answer: Given, 2^(2/3).2^(1/5)

Since, a^m.a^n=a^(m+n)

=(2)^(2/3+1/5)=(2)^((10+3)/15)=2^(13/15)

(ii) (1/(3^3))^7

Answer: Given, (1/(3^3))^7

=(3^-3)^7=3^(-3xx7)=3^-21

(iii) (11^(1/2))/(11^(1/4))

Answer: Given, (11^(1/2))/(11^(1/4))

=(11)^(1/2-1/4)=(11)^((2-1)/4)=11^1/4

(iv) 7^(1/2).8^(1/2)

Answer: Given, 7^(1/2).8^(1/2)

We know that, a^m.b^m=(ab)^m

=(7xx8)^(1/2)=56^(1/2)