How do you write $root5(32)$ as a fractional exponent?

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Answer 1 · 2017-01-23T12:05:07

$32^(1/5)=(2^5)^(1/5)=2^(5xx(1/5))=2^(5/5)=2^1=2$

We can write

$root(5)(32)$

using a fractional exponent this way:

$32^(1/5)$

But we can rewrite $32=2^5$ , and so:

$(2^5)^(1/5)$

We can use the rule that $(x^a)^b=x^(ab)$ to say that:

$(2^5)^(1/5)=2^(5xx(1/5))=2^(5/5)=2^1=2$

So we can write 2 with an exponential as $2^1$

How do you write root5(32)root5(32) as a fractional exponent?