Question

I am having trouble understanding how to do this. Can you help?The directions are to write it in its simplest form. (8a^-3)^-2/3

Answer 1

From the question, we are asked to write

`(8a^(-3))^{-(2)/(3)}`

in its simplest form.

Recall from the law of Indices that;

`(ab)^c=a^cb^c`
`\Rightarrow(8a^(-3))^{-(2)/(3)}=8^{-(2)/(3)}*(a^(-3))^{-(2)/(3)}`

Also, recall that;

`a^(-m)=(1)/(a^m),\text{ }(a^m)^n=a^(m* n)`
`\Rightarrow8^{-(2)/(3)}*(a^(-3))^{-(2)/(3)}=\frac{1}{8^{(2)/(3)}}* a^{-3*-(2)/(3)}=\frac{1}{(\sqrt[3]{8})^2}* a^2=(1)/(4)* a^2=(a^2)/(4)`

In the simplest form, the answer is (a^2)/4.