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

The solution to ((a^{2/3})/(b^{4/3)})^{3/4} is (a^{1/2})/b

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

simplify

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

\frac{a ^{\frac{1}{2}}}{b}

Solution steps

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

Apply exponent rule:

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

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

Simplify

(a^{\frac{2}{3}})^{\frac{3}{4}} : a^{\frac{1}{2}}

= \frac{a ^{\frac{1}{2}}}{( b ^{\frac{4}{3}} ) ^{\frac{3}{4}}}

Simplify

(b^{\frac{4}{3}})^{\frac{3}{4}} : b

= \frac{a ^{\frac{1}{2}}}{b}

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What is ((a^{2/3})/(b^{4/3)})^{3/4} ?
The solution to ((a^{2/3})/(b^{4/3)})^{3/4} is (a^{1/2})/b