Question

Find the value of
(512)*-2/9​

Answer 1

Answer:

⬇️

113.7777777777.........

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Answer 2

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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