Question

find the value of 512 power minus 2 by 9​

Answer 1

1/4 is the right answer.

Answer 2

ᴀɴsᴡᴇʀ

$\bullet\: \: \large\sf\purple{(512)^ \frac{ - 2}{9} \: }$

$\implies \: \: \sf \frac{1}{ {(512)}^{ \frac{2}{9} } } \\ \\ \implies \sf \: \: \frac{1}{ {512}^{ {2}^{ \frac{1}{9} } } } \\ \\ \implies \: \: \sf \frac{1}{ \sqrt[9]{ {512}^{2} } } \\ \\ \implies \: \: \sf \frac{1}{ \sqrt[9]{512 \times 512} } \\ \\ \implies \: \sf \: \frac{1}{ \sqrt[9]{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 } } \\ \\ \implies \: \large{\sf{\red{\fbox{\frac{1}{4}}}}}$

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