Question

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

Answer 1

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:

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

Answer 2

So we need to write (8a^-3)^-2/3 in the simplest form. To solve the problem what we must know is that the powers can multiply or: (a^b)^c=a^(b*c). Now we can solve our problem: (8^-2/3)*(a^-3*(-2/3) ) and we can see that 8=2^3 and when we plug that in we get: 2^(3*(-2/3)) * (a^-3*(-2/3) ) and nnow we can write: (2^-2)*(a^-2)=(1/2^2)*(1/a^2)=1/(4*a^2).