Class 7 Maths

# Exponents and Powers

## Exercise 13.2

Question 1: Using laws of exponents simplify and write the answer in exponential form:

(a) 3^2 xx 3^4 xx 3^8

Answer: 3^2 xx 3^4 xx 3^8

= 3^(2 + 4 + 8) = 3^14

(b) 6^15 ÷ 6^10

Answer: 6^15 ÷ 6^10 = 6^(15 – 10) = 6^5

(c) a^3 xx a^2

Answer: a^3 xx a^2 = a^(3 + 2) = a^5

(d) 7^x \xx 7^2

Answer: 7^x \xx 7^2 = 7^(x + 2)

(e) (5^2)^3 xx 5^3

Answer: (5^2)^3 xx 5^3 = 5^6 xx 5^3

= 5^(6 + 3)= 5^9

(f) 2^5 xx 5^5

Answer: 2^5 xx 5^5x = (2 xx 5)^5 = 10^5

(g) a^4 xx b^4

Answer: a^4 xx b^4 = (ab)^4

(h) (3^4)^4

Answer: (3^4)^4 = 3^16

(i) (2^20 ÷ 2^15) xx 2^3

Answer: (2^20 ÷ 2^15) xx 2^3 = [2^(20 – 15)] xx 2^3

= 2^5 xx 2^3 = 2^(5 + 3) = 2^8

(j) 8^t ÷8^2

Answer: 8^t ÷ 8^2 = 8^(t - 2)

Question 2: Simplify and express each of the following in exponential form:

(a) (2^3xx3^4xx4)/(3xx32)

Answer: =(2^3xx3^4xx2^2)/(3xx2^5)

=(2^(3+2)xx3^4)/(3xx2^5)

=(2^5xx3^(4-1))/(2^5)

=2^(5-5)xx3^3=2^0xx3^3=3^3

(b) ((5^2)^3xx5^4)÷5^7

Answer: =(5^6xx5^4)÷5^7

=(5^(6+4))÷5^7=5^(10)÷5^7

=5^(10-7)=5^3

(c) (3xx7^2xx11^8)/(21xx11^3)

Answer: =(3xx7^2xx11^8)/(3xx7xx11^3)

=3^(1-1)xx7^(2-1)xx11^(8-3)

=3^0xx7^1xx11^5=7xx11^5

(d) (3^7)/(3^4xx3^3)

Answer: =(3^7)/(3^(4+3))=(3^7)/(3^7)

=3^(7-7)=3^0=1

(e) 2^0+3^0+4^0

Answer: =1+1+1=3

(f) 2^0xx3^0xx4^0

Answer: =1xx1xx1=1

(g) (3^0+2^0)xx5^0

Answer: =(1+1)xx1=2xx1=2

(h) (2^8xxa^5)/(4^3xxa^3)

Answer: =(2^8xxa^(5-3))/((2^2)^3)

=(2^8xxa^2)/(2^6)=2^(8-6)xxa^2

=2^2xxa^2=(2a)^2

(i) (4^5xxa^8b^3)/(4^5xxa^5b^2)

Answer: =4^(5-5)xxa^(8-5)xxb^(3-2)

=4^0xxa^3xxb^1=a^3b

(j) (2^3xx2)^2

Answer: =2^(3xx2)xx2^2=2^6xx2^2

=2^(6+2)=2^8

Question 3: Say true or false and justify your answer:

1. 10 xx 10^11 = 100^11

Answer: False, because first number will have 12 zeroes while the second number will have 22 zeroes at the end.
2. 2^3 < 5^2

Answer: False, because first number is 8 while second number is 25.
3. 2^3 xx 3^2 = 6^5

Answer: False, because 6^5 = (2 xx 3)^5 = 2^5 xx 3^5
4. 3^0 = 1000^0

Answer: True, because both are equal to 1.

Question 4: Express each of the following as a product of prime factors only in exponential form:

(a) 108 xx 192

Answer: 108 xx 192 = (2 xx 2 xx 3 xx 3 xx 3) xx (2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 3)

= 2^2xx 3^3 xx 2^6 xx 3 = 2^(2 + 6) xx 3^(3 + 1) = 2^8 xx 3^4

(b) 270

Answer: 270 = 2 xx 3^3 xx 5

(c) 729 xx 64

Answer: 729 xx 64 = 3^6 xx 2^8

(d) 768

Answer: 768 = 2^8 xx 3

Question 5: Simplify

(a) ((2^5)^2xx7^3)/(8^3xx7)

Answer: =(2^(5xx2)xx7^(3-1))/((2^3)^3)

=(2^(10)xx7^2)/(2^9)=2^(10-9)xx7^2=2xx7^2

(b) (25xx5^2xxt^8)/(8^3xxt^4)

Answer: =(5^2xx5^2xxt^(8-4))/((2^3)^3)

=(5^(2+2)xxt^4)/(2^9)=(5^4xxt^4)/(2^9)

(c) (3^5xx10^5xx25)/(5^7xx6^5)

Answer: =(3^5xx(2xx5)^5xx5^2)/(5^7xx(2xx3)^5)

=(3^5xx2^5xx5^5xx5^2)/(5^7xx2^5xx3^5)

=3^(5-5)xx2^(5-5)xx5^(5+2-7)

=3^0xx2^0xx5^0=1