What is (((a^2))/b)^7*(((a^3*b^2))/((c^3)))^4 ?

The solution to (((a^2))/b)^7*(((a^3*b^2))/((c^3)))^4 is (a^{26}b)/(c^{12)}

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simplify (((a^2))/b)^7(((a^3b^2))/((c^3)))^4

simplify

(\frac{( a ^{2} )}{b})^{7} \cdot (\frac{( a ^{3} \cdot b ^{2} )}{( c ^{3} )})^{4}

\frac{a ^{26} b}{c ^{12}}

Solution steps

(\frac{a ^{2}}{b})^{7} (\frac{a ^{3} b ^{2}}{c ^{3}})^{4}

Simplify

(\frac{a ^{2}}{b})^{7} : \frac{a ^{14}}{b ^{7}}

= \frac{a ^{14}}{b ^{7}} (\frac{a ^{3} b ^{2}}{c ^{3}})^{4}

Simplify

(\frac{a ^{3} b ^{2}}{c ^{3}})^{4} : \frac{a ^{12} b ^{8}}{c ^{12}}

= \frac{a ^{14}}{b ^{7}} \cdot \frac{a ^{12} b ^{8}}{c ^{12}}

Apply the fraction rule:

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

= \frac{a ^{14} a ^{12} b ^{8}}{b ^{7} c ^{12}}

Simplify

\frac{b ^{8}}{b ^{7}} : b

= \frac{a ^{14} a ^{12} b}{c ^{12}}

Simplify

a^{14} a^{12} : a^{26}

= \frac{a ^{26} b}{c ^{12}}

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What is (((a^2))/b)^7*(((a^3*b^2))/((c^3)))^4 ?
The solution to (((a^2))/b)^7*(((a^3*b^2))/((c^3)))^4 is (a^{26}b)/(c^{12)}