Question

Which of the following is not equal to 1?

Options

• `(2^3 xx 3^2)/(4 xx 18)`

• `[(-2)^3 xx (-2)^4] ÷ (-2)^7`

• `(3^0 xx 5^3)/(5 xx 25)`

• `2^4/(7^0 + 3^0)^3`

Answer 1

`bb(underline(2^4/(7^0 + 3^0)^3)`

Explanation:

Let us solve the expressions

a. `(2^3 xx 3^2)/(4 xx 18) = (2 xx 2 xx 2 xx 3 xx 3)/(4 xx 18)`

= `(4 xx 18)/(4 xx 18)`

= 1

b. `[(-2)^3 xx (-2)^4] ÷ (-2)^7 = ((-2)^3 xx (-2)^4)/(-2)^7`

= `(-2)^(3+4)/(-2)^7`  ......[∵ a^m × aⁿ = a^m+n]

= `(-2)^7/(-2)^7`  ......`[∵ a^m/a^n = a^(m-n)]`

= 1

c. `(3^0 xx 5^3)/(5 xx 25) = (1 xx 5 xx 5 xx 5)/(5 xx 25)`

= `(5 xx 25)/(5 xx 25)`  ......[∵ a⁰ = 1]

= 1 

d. `2^4/(7^0 + 3^0)^3 = 2^4/(1 + 1)^3`  ......[∵ a⁰ = 1]

= `2^4/2^3` = 2^4–3  ......`[∵ a^m/a^n = a^(m-n), m > n]`

= –2¹ = 2

Hence, `2^4/(7^0 + 3^0)^3` is not equal to 1.