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

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

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

simplify

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

\frac{2 x ^{\frac{1}{3}}}{y ^{\frac{1}{4}}}

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

4^{\frac{1}{2}} = 2

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

Simplify

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

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

Simplify

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

= 2 x^{\frac{1}{3}} \frac{1}{y ^{\frac{1}{4}}}

Simplify

2 x^{\frac{1}{3}} \frac{1}{y ^{\frac{1}{4}}} : \frac{2 x ^{\frac{1}{3}}}{y ^{\frac{1}{4}}}

= \frac{2 x ^{\frac{1}{3}}}{y ^{\frac{1}{4}}}

(- 8 - 2 i) + (8 - i)

lo g_{4} (1 6^{100})

\frac{2 x + 3}{x - 4} + \frac{3}{x + 8}

\frac{7 !}{3 ! \cdot 4 !}

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