What is ((2b^4)/(3a^2b^6))^4 ?

The solution to ((2b^4)/(3a^2b^6))^4 is (16)/(81b^8a^8)

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simplify ((2b^4)/(3a^2b^6))^4

simplify

(\frac{2 b ^{4}}{3 a ^{2} b ^{6}})^{4}

\frac{16}{81 b ^{8} a ^{8}}

Solution steps

(\frac{2 b ^{4}}{3 a ^{2} b ^{6}})^{4}

Apply exponent rule:

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

= \frac{( 2 b ^{4} ) ^{4}}{( 3 a ^{2} b ^{6} ) ^{4}}

Simplify

(2 b^{4})^{4} : 16 b^{16}

= \frac{16 b ^{16}}{( 3 a ^{2} b ^{6} ) ^{4}}

Simplify

(3 a^{2} b^{6})^{4} : 81 a^{8} b^{24}

= \frac{16 b ^{16}}{81 a ^{8} b ^{24}}

Apply exponent rule:

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

\frac{b ^{16}}{b ^{24}} = \frac{1}{b ^{24 - 16}}

= \frac{16}{81 a ^{8} b ^{24 - 16}}

Subtract the numbers:

24 - 16 = 8

= \frac{16}{81 b ^{8} a ^{8}}

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What is ((2b^4)/(3a^2b^6))^4 ?
The solution to ((2b^4)/(3a^2b^6))^4 is (16)/(81b^8a^8)