Find the value of
(512)*-2/9
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(512)^{-\frac{2}{9}}=\frac{1}{4}(512)
−
9
2
=
4
1
Step-by-step explanation:
Given : Expression (512)^{-\frac{2}{9}
To find : The value of the expression ?
Solution :
First we factor 512 so that we get to convert it into the power,
512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2512=2×2×2×2×2×2×2×2×2
512=2^9512=2
9
Substitute in expression,
(512)^{-\frac{2}{9}}=(2^9)^{-\frac{2}{9}}(512)
−
9
2
=(2
9
)
−
9
2
(512)^{-\frac{2}{9}}=(2)^{-\frac{2\times 9}{9}}(512)
−
9
2
=(2)
−
9
2×9
(512)^{-\frac{2}{9}}=(2)^{-2}(512)
−
9
2
=(2)
−2
(512)^{-\frac{2}{9}}=\frac{1}{2^2}(512)
−
9
2
=
2
2
1
(512)^{-\frac{2}{9}}=\frac{1}{4}(512)
−
9
2
=
4
1
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