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Answer:
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Step-by-step explanation:
Answer:
(512)^{-\frac{2}{9}}=\frac{1}{4}(512)−92=41
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=29
Substitute in expression,
(512)^{-\frac{2}{9}}=(2^9)^{-\frac{2}{9}}(512)−92=(29)−92
(512)^{-\frac{2}{9}}=(2)^{-\frac{2\times 9}{9}}(512)−92=(2)−92×9
(512)^{-\frac{2}{9}}=(2)^{-2}(512)−92=(2)−2
(512)^{-\frac{2}{9}}=\frac{1}{2^2}(512)−92=221
(512)^{-\frac{2}{9}}=\frac{1}{4}(512)−92=41
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