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Question
Simplify the following:
`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`
Solution
`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`
= `("a")^("m"xx ("m" - 1/"m") xx (1/("m" + 1))` .....(Using am ÷ an = am -n)
Consider, `"m" xx ("m" - 1/"m") xx (1/"m" + 1)`
= `("m"^2 - 1) xx (1/"m" + 1)`
= `"m"^2 xx (1/"m" + 1) -1 xx (1/"m" + 1)`
= `("m"^2)/("m" + 1) - (1)/("m" + 1)`
= `("m"^2 - 1)/("m" + 1)`
= `(("m" - 1)("m" + 1))/("m" + 1)`
= `"m" - 1("a") "m"xx("m" - 1/"m") xx (1/"m" + 1)`
= am - 1.
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