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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

Sagot :

Given:

Consider the given expression is:

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

By using the quotient property of exponents, we get

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

[tex]=x^{2}y^{-4+2}z^{-6}[/tex]

[tex]=x^{2}y^{-2}z^{-6}[/tex]

By using negative exponent property, we get

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

The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].

Therefore, the correct option is B.

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