# Exponents and Powers

## In Text Questions

Question 1: Express the following:

1. 729 as a power of 3
2. 128 as a power of 2
3. 343 as a power of 7

Answer: (a) 3^6, (b) 2^7, (c) 7^3

Question 2: Simplify and write in exponential form:

(a) 2^5 xx 2^3

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

(b) p^3 xx p^2

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

(c) 4^3 xx 4^2

Answer: 4^3 xx 4^2 = 4^(3 + 2)= 4^5

(d) a^3 xx a^2 xx a^7

Answer: a^3 xx a^2 xx a^7 = a^(3 + 2 + 7) = a^(12)

(e) 5^3 xx 5^7 xx 5^(12)

Answer: 5^3 xx 5^7 xx 5^12 = 5^(3 + 7 + 12) = 5^(22)

(f) ( - 4)^(100) xx ( - 4)^(20)

Answer: ( - 4)^(100) xx ( - 4)^(20) = ( - 4)^(100 + 20) = ( - 4)^(120)

Question 3: Simplify and write in exponential form:

(a) 2^9 ÷ 2^3

Answer: 2^9 ÷ 2^3 = 2^(9 – 3) = 2^6

(b) 10^8 ÷ 10^4

Answer: 10^8 ÷ 10^4 = 10^(8 – 4) = 10^4

(c) 9^(11) ÷ 9^7

Answer: 9^(11) ÷ 9^7 = 9^(11 – 7) = 9^4

(d) 20^(15) ÷ 20^(13)

Answer: 20^(15) ÷ 20^(13) = 20^(15 – 13) = 20^2

(e) 7^(13) ÷ 7^(10)

Answer: 7^(13) ÷ 7^(10) = 7^(13 – 10) = 7^3

Question 4: Simplify and write the answer in exponential form

(a) (6^2)^2

Answer: (6^2)^2 = 6^(2 xx 2)= 6^(12)

(b) (2^2)^(100)

Answer: (2^2)^(100) = 2^(2 xx 100) = 2^(200)

(c) (7^(50))^2

Answer: (7^(50))^2 = 7^(50 xx 2) = 7^(100)

(d) (5^3)^7

Answer: (5^3)^7 = 5^(3 xx 7) = 5^(21)

Question 5: Put into another form using a^m xx b^m = (ab)^m:

(a) 4^3 xx 2^3

Answer: 4^3 xx 2^3 = (4 xx 2)^3 = 8^3

(b) 2^5 xx b^5

Answer: 2^5 xx b^5 = (2 xx b)^5 = (2b)^5

(c) a^2 xx t^2

Answer: a^2 xx t^2 = (at)^2

(d) 5^6 xx ( - 2)^6

Answer: 5^6 xx ( - 2)^6 = (- 10)^6

(e) ( - 2)^4 xx ( - 3)^4

Answer: ( - 2)^4 xx ( - 3)^4 = 6^4

Question 6: Put into another form using: a^m÷b^m=(a/b)^m

(a) 4^5 ÷ 3^5

Answer: 4^5÷3^5=(4/3)^5

(b) 2^5 ÷ b^5

Answer: 2^5÷b^5=(2/b)^5

(c) ( - 2)^3 ÷ b^3

Answer: (-2)^3÷b^3=(-2/b)^3

(d) p^4 ÷ q^4

Answer: p^4÷q^4=(p/q)^4

(e) 5^6 ÷ ( - 2)^6

Answer: 5^6÷(-2)^6=(-5/2)^6

Question 7: Expand by expressing powers of 10 in the exponential form:

(a) 172

Answer: 1 xx 10^2 + 7 xx 10^1 + 2 xx 10^0

(b) 5,643

Answer: 5 xx 10^3 + 6 xx 10^2 + 4 xx 10^1 + 3 xx 10^0

(c) 56,439

Answer: 5 xx 10^4 + 6 xx 10^3 + 4 xx 10^2 + 3 xx 10^1 + 9 xx 10^0

(d) 1,76,428

Answer: 1 xx 10^5 + 7 xx 10^4 + 6 xx 10^3 + 4 xx 10^2 + 2 xx 10^1 + 8 xx 10^0