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

The solution to ((4m^5n^2)/(m^2n))^3 is 64m^9n^3

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

simplify

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

64 m^{9} n^{3}

Solution steps

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

Apply exponent rule:

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

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

Simplify

(4 m^{5} n^{2})^{3} : 64 m^{15} n^{6}

= \frac{64 m ^{15} n ^{6}}{( m ^{2} n ) ^{3}}

Simplify

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

= \frac{64 m ^{15} n ^{6}}{m ^{6} n ^{3}}

Apply exponent rule:

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

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

= \frac{64 n ^{6} m ^{15 - 6}}{n ^{3}}

Subtract the numbers:

15 - 6 = 9

= \frac{64 m ^{9} n ^{6}}{n ^{3}}

Apply exponent rule:

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

\frac{n ^{6}}{n ^{3}} = n^{6 - 3}

= 64 m^{9} n^{6 - 3}

Subtract the numbers:

6 - 3 = 3

= 64 m^{9} n^{3}

(x - y) \cdot (x - y)

(2 x + y)^{2} - (3 y - z)^{2}

\frac{8}{3} - \frac{1}{6}

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