Simplify (x^3y^6)^(1/2)

${(x^{3} y^{6})}^{\frac{1}{2}}$

Apply the product rule to $x^{3} y^{6}$ .

${(x^{3})}^{\frac{1}{2}} {(y^{6})}^{\frac{1}{2}}$

Multiply the exponents in ${(x^{3})}^{\frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{3 (\frac{1}{2})} {(y^{6})}^{\frac{1}{2}}$

Combine $3$ and $\frac{1}{2}$ .

$x^{\frac{3}{2}} {(y^{6})}^{\frac{1}{2}}$

Multiply the exponents in ${(y^{6})}^{\frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{3}{2}} y^{6 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

$x^{\frac{3}{2}} y^{2 \cdot 3 \frac{1}{2}}$

Rewrite the expression.

$x^{\frac{3}{2}} y^{3}$

Reorder factors in $x^{\frac{3}{2}} y^{3}$ .

$y^{3} x^{\frac{3}{2}}$