How do you simplify ${(\frac{2 a^{4} b^{6}}{4 a^{2}})}^{4}$ $(\frac { 2a ^ { 4} b ^ { 6} } { 4a ^ { 2} } ) ^ { 4}$ ?

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How do you simplify ${(\frac{2 a^{4} b^{6}}{4 a^{2}})}^{4}$ $(\frac { 2a ^ { 4} b ^ { 6} } { 4a ^ { 2} } ) ^ { 4}$ ?

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Answer 1 · 2018-03-14T22:38:36

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Explanation:

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

Since its multiplication you can manipulate the $\frac{a^{4}}{a^{2}}$ $a^4/a^2$ and just get $a^{2}$ $a^2$ such as the rule says $\frac{a^{4}}{a^{2}} = a^{4 - 2}$ $a^4/a^2=a^(4-2)$

and so you get

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

$= \frac{a^{2 \cdot 4} b^{6 \cdot 4}}{2^{4}}$ $=(a^(2*4)b^(6*4))/2^4$

$= \frac{a^{8} b^{24}}{32}$ $=(a^8b^24)/32$

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How do you simplify ${(\frac{2 a^{4} b^{6}}{4 a^{2}})}^{4}$ $(\frac { 2a ^ { 4} b ^ { 6} } { 4a ^ { 2} } ) ^ { 4}$ ?

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