Question

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

A. Negative 4 x Superscript 4 Baseline y Superscript 6
B. Negative 8 x Superscript 4 Baseline y Superscript 6
C. StartFraction 4 x Superscript 4 Baseline Over y Superscript 6 EndFraction
D. StartFraction 8 x Superscript 4 Baseline Over y Superscript 6 Baseline EndFraction

Answer 1

c

Explanation:

took test

Answer 2

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

Explanation:

Fractional Powers

The expression

`\sqrt[m]{y^n}=y^{(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 )^(1)/(2)`

It's equivalent to

`(16)^(1)/(2)(x^8)^(1)/(2)(y^(-12))^(1)/(2)`

`=(4)(x^4)(y^(-6))`

`=\displaystyle (4x^4)/(y^(6))`

This corresponds to the option

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