Question

Can someone help with this problem please.

(4^1/2•2^1/3)^-8

I'm a bit confused..

Answer 1

When you raise something to a fractional power, the number in the denominator tells you what root to solve for and the numerator is what you raise the final number to.

EXAMPLE:
\[x ^{\frac{ 1 }{ 2 }}=(\sqrt[2]{x})^{1}=\sqrt{x}\]
As you can see in the example above, having \[\frac{ 1 }{ 2 }\] in the exponent, you first find the square root of x and then raise it to the power of 1....which gives you an answer of square root of x. And if a 3 was to replace the 2, you'd solve for the cube root and if it were replaced by 4 you'd solve for the 4th root....and so on.

When numbers are raised to a negative exponent value, that means whatever it is that is being raised to that negative exponent value would have to move to the denominator, where the exponent changes from negative to positive and you solve it like a regular exponent function.
EXAMPLES:
\[x ^{-1}=\frac{ 1 }{ x^{1} }=\frac{ 1 }{ x }\]
\[x^{-3}=\frac{ 1 }{ x ^{3} }\]