leiana_chung

Question

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

So far I have this.

= (8^-2/3)(a^3(-2/3))
=(8^-2/3)(a^2)
=((2^3)^-2/3)(a^2)
=(2^-2)(a^2)

And this is where I am stuck, can someone explain how to do the rest of the steps?

Answer 1

I think the next step is this

=(1/2^2)(a^2)
=(1/4)(a^2)

But I do need help with this now.

Answer 2

Note that since 8 = 2^3,

8a^-3 = 2^3/a^3 = (2/a)^3
so, (8a^-3)^-2/3 = (a/2)^2 = a^2/4

You are done, and you are correct.

Answer 3

actually Nickie; you are on the right path; if you multiply the (1/4) with the (a^2), you'll get a^2/4, which is the right answer

Answer 4

Thanks, Steve! Always knew I count on YOU, Steve! *wheezes*