Question

Help me turn this term into simplest form:
\[(8a^-3)^\dfrac{-2}{3}\]
\[(\dfrac{8}{a^3})^\dfrac{-2}{3}\]

Answer 1

\[\left(\frac{x}{y}\right)^m=\frac{x^m}{y^{m}}\]

Answer 2

\[\frac{8^\frac{-2}{3}}{a^{3}}\]
Um, wait how would I do it for the denominator?
\[3*\frac{-2}{3} = -2\]
\[\frac{8^\frac{-2}{3}}{a^{-2}}?\]

Answer 3

that's right
\[(8/a^3)^{−2/3}=\frac{8^{-2/3}}{a^{3\times{-2/3}}}=\frac{8^{-2/3}}{a^{-2}}\]


now to simplify the numerator , can you change 8 into something^3?

Answer 4

\[2^3 = 8\]

Answer 5

yeah ,

Answer 6

Wait! I get it.
3 * -2/3 = -2
So:
\[\frac{2^{-2}}{a^{-2}}\]

Answer 7

very good

Answer 8

now you can simplify further

\[\frac{x^n}{y^n}=\left(\frac{x}{x}\right)^n\]

and \(\left(\dfrac{x}{y}\right)^{-p}=\left(\dfrac{y}{x}\right)^p\)

Answer 9

\[\frac{2^{-2}}{a^{-2}}\Rightarrow \frac{a^2}{4}?\]

Answer 10

*\[\frac{x^n}{y^n}=\left(\frac{x}{y}\right)^n\]

Answer 11

That is right you've got it!

Answer 12

Thank you for teaching me :-).