How do you simplify $(49/81) ^ (-1/2)$ ?

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Answer 1 · 2018-05-03T16:16:23

9/7

$1/sqrt(49/81)$ = $1/(7/9)$ = $9/7$

Answer 2 · 2018-05-03T16:17:00

$9/7$

$(a/b)^(m/n)=root(n)((a/b)^m)$
If $m/n$ is negative
$(a/b)^-(m/n)=1/root(n)((a/b)^m)$

SO:
$(49/81)^(-1/2)=1/sqrt((49/81)^1)=1/(7/9)=9/7$

Answer 3 · 2018-05-03T16:19:00

Simplified we should get $+-9/7$

To solve this we need to remember that $x^{1/2}= sqrt(x)$
Aslo $x^(-1)=1/x$
And lastly we should recognise that
$49=7^2$ and $81=9^2$

If we do, it's quite straightforward:
$(49/81)^-(1/2)=(9^2/7^2)^(1/2)=(9/7)^(2*1/2)=9/7$

As $(-sqrt(x))^2=(sqrt(x))^2=x$

the full simplification should then be $+-9/7$

How do you simplify (49/81) ^ (-1/2)(49/81) ^ (-1/2)?