What is ((x^2y)/(y^5))^{2/3} ?

The solution to ((x^2y)/(y^5))^{2/3} is ((x^4)/(y^8))^{1/3}

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simplify ((x^2y)/(y^5))^{2/3}

simplify

(\frac{x ^{2} y}{y ^{5}})^{\frac{2}{3}}

(\frac{x ^{4}}{y ^{8}})^{\frac{1}{3}}

Solution steps

(\frac{x ^{2} y}{y ^{5}})^{\frac{2}{3}}

Apply exponent rule:

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

= \frac{( x ^{2} y ) ^{\frac{2}{3}}}{( y ^{5} ) ^{\frac{2}{3}}}

Simplify

(x^{2} y)^{\frac{2}{3}} : x^{\frac{4}{3}} y^{\frac{2}{3}}

= \frac{x ^{\frac{4}{3}} y ^{\frac{2}{3}}}{( y ^{5} ) ^{\frac{2}{3}}}

Simplify

(y^{5})^{\frac{2}{3}} : y^{\frac{10}{3}}

= \frac{x ^{\frac{4}{3}} y ^{\frac{2}{3}}}{y ^{\frac{10}{3}}}

Apply exponent rule:

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

\frac{y ^{\frac{2}{3}}}{y ^{\frac{10}{3}}} = \frac{1}{y ^{\frac{10}{3} - \frac{2}{3}}}

= \frac{x ^{\frac{4}{3}}}{y ^{\frac{10}{3} - \frac{2}{3}}}

Subtract the numbers:

\frac{10}{3} - \frac{2}{3} = \frac{8}{3}

= \frac{x ^{\frac{4}{3}}}{y ^{\frac{8}{3}}}

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

= (\frac{x ^{4}}{y ^{8}})^{\frac{1}{3}}

x^{2} + 12 x - 2 = 0

x \geq 1 or x < - 1

- 2 v^{2} - 7 = 47 v^{2}

x + 2 = x - 2

x^{5} > x^{3}

What is ((x^2y)/(y^5))^{2/3} ?
The solution to ((x^2y)/(y^5))^{2/3} is ((x^4)/(y^8))^{1/3}