Simplify (9x^(2/5)y^(3/5))^(5/2)

${(9 x^{\frac{2}{5}} y^{\frac{3}{5}})}^{\frac{5}{2}}$

Step 1

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

Apply the product rule to $9 x^{\frac{2}{5}} y^{\frac{3}{5}}$ .

${(9 x^{\frac{2}{5}})}^{\frac{5}{2}} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Apply the product rule to $9 x^{\frac{2}{5}}$ .

$9^{\frac{5}{2}} {(x^{\frac{2}{5}})}^{\frac{5}{2}} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Step 2

Simplify the expression.

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

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

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

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the expression.

Raise $3$ to the power of $5$ .

$243 {(x^{\frac{2}{5}})}^{\frac{5}{2}} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

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

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

$243 x^{\frac{2}{5} \cdot \frac{5}{2}} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$243 x^{\frac{2}{5} \cdot \frac{5}{2}} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Rewrite the expression.

$243 x^{\frac{1}{5} \cdot 5} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$243 x^{\frac{1}{5} \cdot 5} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Rewrite the expression.

$243 x^{1} {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Step 5

Simplify.

$243 x {(y^{\frac{3}{5}})}^{\frac{5}{2}}$

Step 6

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

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

$243 x y^{\frac{3}{5} \cdot \frac{5}{2}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$243 x y^{\frac{3}{5} \cdot \frac{5}{2}}$

Rewrite the expression.

$243 x y^{3 (\frac{1}{2})}$

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

$243 x y^{\frac{3}{2}}$

Simplify (9x^(2/5)y^(3/5))^(5/2)

Related Questions

Support LCMGCF.com by disabling your adblocker.