Question

$find \: the \: value \: of(512) \frac{ - 2}{9}$
​

Answer 1

Answer:

$(512)^{\frac{-2}{9}}=\frac{1}{4}$

Step-by-step explanation:

We have ,

2| 512

_________

2| 256

_________

2| 128

_________

2| 64

_________

2| 32

_________

2| 16

_________

2| 8

_________

2| 4

__________

***2

$512= 2^{9}$

$Now, \\(512)^{\frac{-2}{9}}\\=(2^{9})^{\frac{-2}{9}}\\=2^{9\times \left(\frac{-2}{9}\right)}\\=2^{-2}\\=\frac{1}{2^{2}}\\=\frac{1}{4}$

Therefore,

$(512)^{\frac{-2}{9}}=\frac{1}{4}$

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