Solve the Rational Equation for x x^(3/2)=125

$x^{\frac{3}{2}} = 125$

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 125^{\frac{2}{3}}$

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 125^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 125^{\frac{2}{3}}$

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 125^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 125^{\frac{2}{3}}$

Rewrite the expression.

$x^{1} = 125^{\frac{2}{3}}$

Simplify.

$x = 125^{\frac{2}{3}}$

Simplify the right side.

Simplify $125^{\frac{2}{3}}$ .

Simplify the expression.

Rewrite $125$ as $5^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 5^{2}$

Raise $5$ to the power of $2$ .

$x = 25$