Question

Which expression is equivalent to (16x^8y^-12)^1/2

Answer 1

Answer:

The equivalent expression is $\Rightarrow \dfrac{4x^4}{y^6}$

Step-by-step explanation:

Given: $(16x^8y^{-12})^{1/2}$

We need to simplify the expression. We will distribute radical with each term inside the parentheses.

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

Distribute the radical

$\Rightarrow 16^{1/2}\cdot x^{8\cdot 1/2\cdot y^{-12\cdot 1/2}$

$\Rightarrow 4\cdot x^4\cdot y^{-6}$

$\Rightarrow 4x^4y^{-6}$

Now we will simplify the negative exponent.

$\Rightarrow \dfrac{4x^4}{y^6}$

Hence, The equivalent expression is $\Rightarrow \dfrac{4x^4}{y^6}$