How do you simplify (49/81) ^ (-1/2)(4981)−12?

3 Answers
Bella
May 3, 2018

9/7

Explanation:

1/sqrt(49/81)1√4981 =1/(7/9)179 = 9/797

KB.
May 3, 2018

9/797

Explanation:

(a/b)^(m/n)=root(n)((a/b)^m)(ab)mn=n√(ab)m
If m/nmn is negative
(a/b)^-(m/n)=1/root(n)((a/b)^m)(ab)−(mn)=1n√(ab)m

SO:
(49/81)^(-1/2)=1/sqrt((49/81)^1)=1/(7/9)=9/7(4981)−12=1√(4981)1=179=97

Roy Ø.
May 3, 2018

Simplified we should get +-9/7±97

Explanation:

To solve this we need to remember that x^{1/2}= sqrt(x)x12=√x
Aslo x^(-1)=1/xx−1=1x
And lastly we should recognise that
49=7^249=72 and 81=9^281=92

If we do, it's quite straightforward:
(49/81)^-(1/2)=(9^2/7^2)^(1/2)=(9/7)^(2*1/2)=9/7(4981)−(12)=(9272)12=(97)2⋅12=97

As (-sqrt(x))^2=(sqrt(x))^2=x(−√x)2=(√x)2=x

the full simplification should then be +-9/7±97

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