Solve for y y^(5/2)=243

$y^{\frac{5}{2}} = 243$

Step 1

Raise each side of the equation to the power of $\frac{2}{5}$ to eliminate the fractional exponent on the left side.

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

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${(y^{\frac{5}{2}})}^{\frac{2}{5}}$ .

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

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

$y^{\frac{5}{2} \cdot \frac{2}{5}} = 243^{\frac{2}{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$y^{\frac{5}{2} \cdot \frac{2}{5}} = 243^{\frac{2}{5}}$

Rewrite the expression.

$y^{\frac{1}{2} \cdot 2} = 243^{\frac{2}{5}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = 243^{\frac{2}{5}}$

Rewrite the expression.

$y^{1} = 243^{\frac{2}{5}}$

Simplify.

$y = 243^{\frac{2}{5}}$

Simplify the right side.

Simplify $243^{\frac{2}{5}}$ .

Simplify the expression.

Rewrite $243$ as $3^{5}$ .

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3^{2}$

Raise $3$ to the power of $2$ .

$y = 9$