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

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

Step 1

Apply the product rule to $x^{\frac{1}{2}} y^{3}$ .

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

Step 2

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x^{3} {(y^{3})}^{6}$

Step 3

Multiply the exponents in ${(y^{3})}^{6}$ .

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

$x^{3} y^{3 \cdot 6}$

Multiply $3$ by $6$ .

$x^{3} y^{18}$