Question

Simplify the expression. x4y−4z−2x2y−2z4 y2x2z6 the fraction with numerator y squared and denominator x squared z to the 6th power x2y2z6 the fraction with numerator x squared and denominator y squared z to the 6th power x2y2z6 the fraction with numerator x squared y squared and denominator z to the 6th power y2z6x2

Answer 1

Given:

Consider the given expression is:

$\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}$

To find:

The simplified form of the given expression.

Solution:

We have,

$\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}$

By using the quotient property of exponents, we get

$=x^{4-2}y^{-4-(-2)}z^{-2-4}$              $\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right]$

$=x^{2}y^{-4+2}z^{-6}$

$=x^{2}y^{-2}z^{-6}$

By using negative exponent property, we get

$=\dfrac{x^{2}}{y^{2}z^{6}}$           $\left[\because a^{-n}=\dfrac{1}{a^n}\right]$

The simplified form of the given expression is $\dfrac{x^{2}}{y^{2}z^{6}}$.

Therefore, the correct option is B.