Simplify (x^4y^5)^(3/2)

${(x^{4} y^{5})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $x^{4} y^{5}$ .

${(x^{4})}^{\frac{3}{2}} {(y^{5})}^{\frac{3}{2}}$

Step 2

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

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

$x^{4 (\frac{3}{2})} {(y^{5})}^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{2 (2) \frac{3}{2}} {(y^{5})}^{\frac{3}{2}}$

Cancel the common factor.

$x^{2 \cdot 2 \frac{3}{2}} {(y^{5})}^{\frac{3}{2}}$

Rewrite the expression.

$x^{2 \cdot 3} {(y^{5})}^{\frac{3}{2}}$

Multiply $2$ by $3$ .

$x^{6} {(y^{5})}^{\frac{3}{2}}$

Step 3

Multiply the exponents in ${(y^{5})}^{\frac{3}{2}}$ .

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

$x^{6} y^{5 (\frac{3}{2})}$

Multiply $5 (\frac{3}{2})$ .

Combine $5$ and $\frac{3}{2}$ .

$x^{6} y^{\frac{5 \cdot 3}{2}}$

Multiply $5$ by $3$ .

$x^{6} y^{\frac{15}{2}}$