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

The solution to (4a^2b)^4((-a^3)/(2b))^2 is 64a^{14}b^2

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

simplify

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

64 a^{14} b^{2}

Solution steps

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

Simplify

(4 a^{2} b)^{4} : 256 a^{8} b^{4}

= 256 a^{8} b^{4} (\frac{- a ^{3}}{2 b})^{2}

Simplify

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

= 256 a^{8} b^{4} \frac{a ^{6}}{4 b ^{2}}

Apply the fraction rule:

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

= \frac{256 a ^{8} b ^{4} a ^{6}}{4 b ^{2}}

Factor the number:

256 = 4 \cdot 64

= \frac{4 \cdot 64 a ^{8} b ^{4} a ^{6}}{4 b ^{2}}

Cancel the common factor:

4

= \frac{64 a ^{8} b ^{4} a ^{6}}{b ^{2}}

Simplify

\frac{b ^{4}}{b ^{2}} : b^{2}

= 64 a^{8} b^{2} a^{6}

Simplify

a^{8} a^{6} : a^{14}

= 64 a^{14} b^{2}

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What is (4a^2b)^4((-a^3)/(2b))^2 ?
The solution to (4a^2b)^4((-a^3)/(2b))^2 is 64a^{14}b^2