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Question
If `p/q = (3/2)^2 ÷ (9/4)^0`, find the value of `(p/q)^3`.
Solution
We have, `p/q = (3/2)^2 ÷ (9/4)^0`
⇒ `p/q = (3/2)^2 ÷ 1/1` ......[∵ a0 = 1]
⇒ `p/q = (3/2)^2` ......`[∵ a/b ÷ c/d = a/b xx d/c]`
⇒ `p/q = 3^2/2^2` ......`[∵ (a/b)^n = a^n/b^n]`
⇒ `p/q = 9/4`
On taking cube both sides, we get
`(p/q)^3 = (9/4)^3`
∴ `(p/q)^3 = (9 xx 9 xx 9)/(4 xx 4 xx 4) = 729/64`
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