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

The solution to sqrt(x^3\sqrt{(x^2y)^2)} is x^2sqrt(xy)

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simplify sqrt(x^3\sqrt{(x^2y)^2)}

simplify

x^{3} (x^{2} y)^{2}

x^{2} x y

Solution steps

x^{3} (x^{2} y)^{2}

(x^{2} y)^{2} = x^{2} y

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

Simplify

x^{3} x^{2} y : x^{5} y

= x^{5} y

Apply radical rule:

assuming

a \geq 0, b \geq 0

= y x^{5}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= x^{4} x^{1} y

Apply radical rule:

a \cdot b = a b

= x^{4} x^{1} y

Apply exponent rule:

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

x^{4} = x^{2 \cdot 2} = (x^{2})^{2}

= (x^{2})^{2} x^{1} y

Apply radical rule:

assuming

a \geq 0

(x^{2})^{2} = x^{2}

= x^{2} y x^{1}

Apply radical rule:

a b = a \cdot b,

assuming

a \geq 0, b \geq 0

y x^{1} = x^{1} y

= x^{2} x^{1} y

Apply rule

a^{1} = a

x^{1} = x

= x^{2} x y

- \frac{\frac{- 5}{3}}{( \frac{\frac{3}{4}}{( \frac{7}{2} - \frac{5}{3} )} )}

\frac{1}{2} (\frac{1}{3})

\frac{7 3}{14}

(- 8 x^{5})^{3}

- 4 x + 12

What is sqrt(x^3\sqrt{(x^2y)^2)} ?
The solution to sqrt(x^3\sqrt{(x^2y)^2)} is x^2sqrt(xy)