How do you simplify $\frac{7 a}{\sqrt[5]{4 a^{7} b^{13}}}$ $\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }$ ?

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How do you simplify $\frac{7 a}{\sqrt[5]{4 a^{7} b^{13}}}$ $\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }$ ?

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Answer 1 · 2018-03-28T20:36:13

$\frac{7}{\sqrt[5]{4} a^{\frac{2}{5}} b^{\frac{13}{5}}}$ $7/(root(5)(4)a^(2/5)b^(13/5))$

Explanation:

First, we take the root of each product

$\frac{7 a}{\sqrt[5]{4 a^{7} b^{13}}} = \frac{7 a}{\sqrt[5]{4} \sqrt[5]{a^{7}} \sqrt[5]{b^{13}}}$ $\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }=(7a)/(root(5)(4)root(5)(a^7)root(5)(b^13))$

$\sqrt[a]{b^{c}} = b^{\frac{c}{a}}$ $root(a)(b^c)=b^(c/a)$

$\frac{7 a}{\sqrt[5]{4} \sqrt[5]{a^{7}} \sqrt[5]{b^{13}}} = \frac{7 a}{\sqrt[5]{4} a^{\frac{7}{5}} b^{\frac{13}{5}}}$ $(7a)/(root(5)(4)root(5)(a^7)root(5)(b^13))=(7a)/(root(5)(4)a^(7/5)b^(13/5))$

$\frac{a^{b}}{a^{c}} = a^{b - c}$ $(a^b)/a^c=a^(b-c)$
$a = a^{1}$ $a=a^1$

$\frac{7 a}{\sqrt[5]{4} a^{\frac{7}{5}} b^{\frac{13}{5}}} = \frac{7}{\sqrt[5]{4} a^{\frac{2}{5}} b^{\frac{13}{5}}}$ $(7a)/(root(5)(4)a^(7/5)b^(13/5))=7/(root(5)(4)a^(2/5)b^(13/5))$

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How do you simplify $\frac{7 a}{\sqrt[5]{4 a^{7} b^{13}}}$ $\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }$ ?

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Explanation:

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How do you simplify 7a5√4a7b13\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }?

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How do you simplify $\frac{7 a}{\sqrt[5]{4 a^{7} b^{13}}}$ $\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }$ ?