What is (3x^4y^{-5})^3 ?

The solution to (3x^4y^{-5})^3 is (27x^{12})/(y^{15)}

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simplify (3x^4y^{-5})^3

simplify

(3 x^{4} y^{- 5})^{3}

\frac{27 x ^{12}}{y ^{15}}

Solution steps

(3 x^{4} y^{- 5})^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 x^{4} y^{- 5})^{3} = 3^{3} (x^{4})^{3} (y^{- 5})^{3}

= 3^{3} (x^{4})^{3} (y^{- 5})^{3}

3^{3} = 27

= 27 (x^{4})^{3} (y^{- 5})^{3}

Simplify

(x^{4})^{3} : x^{12}

= 27 x^{12} (y^{- 5})^{3}

Simplify

(y^{- 5})^{3} : \frac{1}{y ^{15}}

= 27 x^{12} \frac{1}{y ^{15}}

Simplify

27 x^{12} \frac{1}{y ^{15}} : \frac{27 x ^{12}}{y ^{15}}

= \frac{27 x ^{12}}{y ^{15}}

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