What is ((x^2yz^0)/(3x^6y^{-4)})^4 ?

The solution to ((x^2yz^0)/(3x^6y^{-4)})^4 is (y^{20})/(81x^{16)}

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simplify ((x^2yz^0)/(3x^6y^{-4)})^4

simplify

(\frac{x ^{2} y z ^{0}}{3 x ^{6} y ^{- 4}})^{4}

\frac{y ^{20}}{81 x ^{16}}

Solution steps

(\frac{x ^{2} y z ^{0}}{3 x ^{6} y ^{- 4}})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x ^{2} y z ^{0} ) ^{4}}{( 3 x ^{6} y ^{- 4} ) ^{4}}

Simplify

(x^{2} y z^{0})^{4} : x^{8} y^{4}

= \frac{x ^{8} y ^{4}}{( 3 x ^{6} y ^{- 4} ) ^{4}}

Simplify

(3 x^{6} y^{- 4})^{4} : \frac{81 x ^{24}}{y ^{16}}

= \frac{x ^{8} y ^{4}}{\frac{81 x ^{24}}{y ^{16}}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{x ^{8} y ^{4} y ^{16}}{81 x ^{24}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{x ^{8}}{x ^{24}} = \frac{1}{x ^{24 - 8}}

= \frac{y ^{16} y ^{4}}{81 x ^{24 - 8}}

Subtract the numbers:

24 - 8 = 16

= \frac{y ^{16} y ^{4}}{81 x ^{16}}

y^{16} y^{4} = y^{20}

= \frac{y ^{20}}{81 x ^{16}}

\frac{( \frac{2}{3} ) ^{2}}{( \frac{2}{3} ) ^{3}}

(65 - 125) \cdot 45

(4 x - y)^{2}

\frac{x ^{2} - 64}{x ^{2} + 16 x + 64}

16 \div 8

What is ((x^2yz^0)/(3x^6y^{-4)})^4 ?
The solution to ((x^2yz^0)/(3x^6y^{-4)})^4 is (y^{20})/(81x^{16)}