Question

Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?

Answer 1

Answer:

C. StartFraction 4 x Superscript 4 Baseline Over y Superscript 6 EndFraction

Step-by-step explanation:

Fractional Powers

The expression

$\sqrt[m]{y^n}=y^{\frac{n}{m}}$

can be used to reduce roots and fractional powers.

Another useful relation is

$(y^n)^m=y^{n.m}$

We are given the expressión

$\left ( 16x^8y^{-12} \right )^\frac{1}{2}$

It's equivalent to

$(16)^\frac{1}{2}(x^8)^\frac{1}{2}(y^{-12})^\frac{1}{2}$

$=(4)(x^4)(y^{-6})$

$=\displaystyle \frac{4x^4}{y^{6}}$

This corresponds to the option  

C. StartFraction 4 x Superscript 4 Baseline Over y Superscript 6 EndFraction