What is (-((4-x^{2/3})^{1/2})/(x^{1/3)})^2 ?

The solution to (-((4-x^{2/3})^{1/2})/(x^{1/3)})^2 is (4-x^{2/3})/(x^{2/3)}

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simplify (-((4-x^{2/3})^{1/2})/(x^{1/3)})^2

simplify

- \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}^{2}

\frac{4 - x ^{\frac{2}{3}}}{x ^{\frac{2}{3}}}

Solution steps

- \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

- \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}^{2} = \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}^{2}

= \frac{( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}}}{x ^{\frac{1}{3}}}^{2}

Apply exponent rule:

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

= \frac{( ( 4 - x ^{\frac{2}{3}} ) ^{\frac{1}{2}} ) ^{2}}{( x ^{\frac{1}{3}} ) ^{2}}

Simplify

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

= \frac{4 - x ^{\frac{2}{3}}}{( x ^{\frac{1}{3}} ) ^{2}}

Simplify

(x^{\frac{1}{3}})^{2} : x^{\frac{2}{3}}

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

\frac{4 x y ^{3}}{x ^{7} y ^{3}}

\frac{1}{6} n (n + 1) (2 n + 1)

\frac{7}{18}

(rs)^{3} - 1

- \frac{3}{4} + \frac{1}{3}

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