Question

Which expression is equivalent to (x superscript one-half baseline y superscript negative one-fourth baseline z) superscript negative 2?

Answer 1

Exponential equations are equation that contain powers or exponents in them. The simplified form of the given expression is $\frac{\sqrt{y}}{xz^2}$

Exponential functions

Given the exponential function expressed as

$(x^{1/2}y^{-1/4}z})^{-2}$

According to the law of indices expressed as

$(a^m)^n= a^{mn}$

Applying this law to the given exponential equation, we will have:

$=(x^{1/2}y^{-1/4}z})^{-2}\\=(x^{1/2})^{-2}(y^{-1/4})^{-2}(z})^{-2}\\=x^{-1}y^{1/2}z^{-2}$

Using the inverse law;

$(x^{1/2}y^{-1/4}z})^{-2}=\frac{1}{x}\sqrt{y}\frac{1}{z^2}\\ (x^{1/2}y^{-1/4}z})^{-2}=\frac{\sqrt{y}}{xz^2}$

Hence the simplified form of the given expression is $\frac{\sqrt{y}}{xz^2}$

Learn more on exponential function here: brainly.com/question/14197900