What is ((3m^4n^5)/(6n^2))^3 ?

The solution to ((3m^4n^5)/(6n^2))^3 is (m^{12}n^9)/8

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simplify ((3m^4n^5)/(6n^2))^3

simplify

(\frac{3 m ^{4} n ^{5}}{6 n ^{2}})^{3}

\frac{m ^{12} n ^{9}}{8}

Solution steps

(\frac{3 m ^{4} n ^{5}}{6 n ^{2}})^{3}

Apply exponent rule:

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

= \frac{( 3 m ^{4} n ^{5} ) ^{3}}{( 6 n ^{2} ) ^{3}}

Simplify

(3 m^{4} n^{5})^{3} : 27 m^{12} n^{15}

= \frac{27 m ^{12} n ^{15}}{( 6 n ^{2} ) ^{3}}

Simplify

(6 n^{2})^{3} : 216 n^{6}

= \frac{27 m ^{12} n ^{15}}{216 n ^{6}}

Cancel the common factor:

27

= \frac{m ^{12} n ^{15}}{8 n ^{6}}

Apply exponent rule:

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

\frac{n ^{15}}{n ^{6}} = n^{15 - 6}

= \frac{m ^{12} n ^{15 - 6}}{8}

Subtract the numbers:

15 - 6 = 9

= \frac{m ^{12} n ^{9}}{8}

(a + b)^{- 1} \cdot (a^{- 1} + b^{- 1})

\frac{1}{sin ^{2} ( a )} - \frac{1}{tan ^{2} ( a )}

(7 v - 9) - 2 (6 v + 9)

\frac{a ^{20}}{a ^{15}}

a - 1 x^{2} - 2 x + 1

What is ((3m^4n^5)/(6n^2))^3 ?
The solution to ((3m^4n^5)/(6n^2))^3 is (m^{12}n^9)/8