can anyone help me with this question
simplify
9^-1/2 x 8^2/3 ?
$\displaystyle 9^{-1/2} \cdot 8^{2/3}$
First, if you have a negative exponent, you can make it positive by putting it in the denominator of a fraction:
$\displaystyle = \frac{1}{9^{1/2}} \cdot 8^{2/3}$
An exponent of 1/2 is the same as square root, so the square root of 9 is 3:
$\displaystyle = \frac{1}{3} \cdot 8^{2/3}$
The 8 to the 2/3 power can be rewritten using the power-of-a-power property:
$\displaystyle = \frac{1}{3} \cdot (8^{1/3})^2$
An exponent of 1/3 is the same as cube root, so the cube root of 8 is 2:
$\displaystyle = \frac{1}{3} \cdot 2^2$
Simplify:
$\displaystyle = \frac{4}{3}$
EDIT: Sorry pickslides!