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`



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