Simplify (9x^4y^6)^(3/2)

${(9 x^{4} y^{6})}^{\frac{3}{2}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $9 x^{4} y^{6}$ .

${(9 x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Apply the product rule to $9 x^{4}$ .

$9^{\frac{3}{2}} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Simplify the expression.

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{3}{2}} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

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

$3^{2 (\frac{3}{2})} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{3}{2})} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Rewrite the expression.

$3^{3} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Simplify the expression.

Raise $3$ to the power of $3$ .

$27 {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Multiply the exponents in ${(x^{4})}^{\frac{3}{2}}$ .

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

$27 x^{4 (\frac{3}{2})} {(y^{6})}^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$27 x^{2 (2) \frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Cancel the common factor.

$27 x^{2 \cdot 2 \frac{3}{2}} {(y^{6})}^{\frac{3}{2}}$

Rewrite the expression.

$27 x^{2 \cdot 3} {(y^{6})}^{\frac{3}{2}}$

Multiply $2$ by $3$ .

$27 x^{6} {(y^{6})}^{\frac{3}{2}}$

Multiply the exponents in ${(y^{6})}^{\frac{3}{2}}$ .

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

$27 x^{6} y^{6 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$27 x^{6} y^{2 (3) \frac{3}{2}}$

Cancel the common factor.

$27 x^{6} y^{2 \cdot 3 \frac{3}{2}}$

Rewrite the expression.

$27 x^{6} y^{3 \cdot 3}$

Multiply $3$ by $3$ .

$27 x^{6} y^{9}$