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:

`(x^4y^(-4)z^(-2))/(x^2y^(-2)z^4)`

To find:

The simplified form of the given expression.

Solution:

We have,

`(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 (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

`=(x^(2))/(y^(2)z^(6))`
`\left[\because a^(-n)=(1)/(a^n)\right]`

The simplified form of the given expression is
`(x^(2))/(y^(2)z^(6))`.

Therefore, the correct option is B.