What is (5a^m(5b^m)^2)/((a^2m)^2) ?

The solution to (5a^m(5b^m)^2)/((a^2m)^2) is (125a^{m-4}b^{2m})/(m^2)

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simplify (5a^m(5b^m)^2)/((a^2m)^2)

simplify

\frac{5 a ^{m} ( 5 b ^{m} ) ^{2}}{( a ^{2} m ) ^{2}}

\frac{125 a ^{m - 4} b ^{2 m}}{m ^{2}}

Solution steps

\frac{5 a ^{m} ( 5 b ^{m} ) ^{2}}{( a ^{2} m ) ^{2}}

Simplify

(a^{2} m)^{2} : a^{4} m^{2}

= \frac{5 a ^{m} ( 5 b ^{m} ) ^{2}}{a ^{4} m ^{2}}

Apply exponent rule:

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

\frac{a ^{m}}{a ^{4}} = a^{m - 4}

= \frac{5 a ^{m - 4} ( 5 b ^{m} ) ^{2}}{m ^{2}}

Simplify

5 a^{m - 4} (5 b^{m})^{2} : 125 a^{m - 4} b^{2 m}

= \frac{125 a ^{m - 4} b ^{2 m}}{m ^{2}}

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What is (5a^m(5b^m)^2)/((a^2m)^2) ?
The solution to (5a^m(5b^m)^2)/((a^2m)^2) is (125a^{m-4}b^{2m})/(m^2)