Write (8a^-3)^-2/3 in a simplest form.

Asked by maham237 @ 17/12/2020 in Mathematics viewed by 363 People

Write (8a^-3)^-2/3 in a simplest form.
a. a^2/4
b. 4a^2
c. 1/4a^2
d. none of these

Answered by maham237 @ 17/12/2020

For this case we have the following expression:

$(8a^{-3})^{-\frac{2}{3}}$

For power properties we have:

$(8^{-\frac{2}{3}} a^{-3*-\frac{2}{3}})$

Rewriting the exponents of the expression we have:

$(8^{-\frac{2}{3}} a^{3*\frac{2}{3}})$

$(8^{-\frac{2}{3}} a^2)$

$(\frac{1}{8^{\frac{2}{3}}} a^2)$

Using the cubic root we have:

$(\frac{1}{\sqrt[3]{8^2}} a^2)$

$(\frac{1}{\sqrt[3]{64}} a^2)$

$(\frac{1}{\sqrt[3]{4^3}} a^2)$

Simplifying the expression we have:

$(\frac{1}{4} a^2)$

Answer:

The equivalent expression is given by:

$(\frac{1}{4} a^2)$

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