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Popular >

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

Solution

simplify

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

Solution

\frac{a ^{6}}{b ^{9}}

Solution steps

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

Apply exponent rule:

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

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

Simplify

(a^{2} b)^{3} : a^{6} b^{3}

= \frac{a ^{6} b ^{3}}{( b ^{4} ) ^{3}}

Simplify

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

= \frac{a ^{6} b ^{3}}{b ^{12}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{b ^{3}}{b ^{12}} = \frac{1}{b ^{12 - 3}}

= \frac{a ^{6}}{b ^{12 - 3}}

Subtract the numbers:

12 - 3 = 9

= \frac{a ^{6}}{b ^{9}}

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Frequently Asked Questions (FAQ)

What is ((a^2b)/(b^4))^3 ?
The solution to ((a^2b)/(b^4))^3 is (a^6)/(b^9)