What is (25x^{-6}y^2)^{1/2} ?

The solution to (25x^{-6}y^2)^{1/2} is (5y)/(x^3)

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simplify (25x^{-6}y^2)^{1/2}

simplify

(25 x^{- 6} y^{2})^{\frac{1}{2}}

\frac{5 y}{x ^{3}}

Solution steps

(25 x^{- 6} y^{2})^{\frac{1}{2}}

Apply exponent rule:

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

(25 x^{- 6} y^{2})^{\frac{1}{2}} = 2 5^{\frac{1}{2}} (x^{- 6})^{\frac{1}{2}} (y^{2})^{\frac{1}{2}}

= 2 5^{\frac{1}{2}} (x^{- 6})^{\frac{1}{2}} (y^{2})^{\frac{1}{2}}

2 5^{\frac{1}{2}} = 5

= 5 (x^{- 6})^{\frac{1}{2}} (y^{2})^{\frac{1}{2}}

Simplify

(x^{- 6})^{\frac{1}{2}} : \frac{1}{x ^{3}}

= 5 \cdot \frac{1}{x ^{3}} (y^{2})^{\frac{1}{2}}

Simplify

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

= 5 \cdot \frac{1}{x ^{3}} y

Simplify

5 \cdot \frac{1}{x ^{3}} y : \frac{5 y}{x ^{3}}

= \frac{5 y}{x ^{3}}

\frac{( 1 + 3 i )}{( 1 + i )}

\frac{9}{4} \cdot 2

\frac{36}{121}

18 x^{3} + 29 x^{2} + 3 x

(a b^{- 1} + b a^{- 1}) (a^{- 2} + b^{- 2})^{- 1}