What is sqrt(x^3*y^{-2)} ?

The solution to sqrt(x^3*y^{-2)} is (xsqrt(x))/y

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simplify sqrt(x^3*y^{-2)}

simplify

x^{3} \cdot y^{- 2}

\frac{x x}{y}

Solution steps

x^{3} y^{- 2}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

x^{3} y^{- 2} = x^{3} y^{- 2}

= x^{3} y^{- 2}

Simplify

x^{3} : x x

= x x y^{- 2}

Simplify

y^{- 2} : \frac{1}{y}

= x x \frac{1}{y}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x x \cdot 1}{y}

Apply rule:

a \cdot 1 = a

x x \cdot 1 = x x

= \frac{x x}{y}

x^{2} - 1 + 2 a - a^{2}

∣ x ∣^{2} + 7 ∣ x ∣ + 12

x^{3} - x - 24

4 x^{2} y - 3 x^{3} y^{2} - x^{4}

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