Solve for x cube root of x^4=625

$\sqrt[3]{x^{4}} = 625$

Step 1

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{x^{4}}}^{3} = 625^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{4}}$ as $x^{\frac{4}{3}}$ .

${(x^{\frac{4}{3}})}^{3} = 625^{3}$

Simplify the left side.

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

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

$x^{\frac{4}{3} \cdot 3} = 625^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{\frac{4}{3} \cdot 3} = 625^{3}$

Rewrite the expression.

$x^{4} = 625^{3}$

Simplify the right side.

Raise $625$ to the power of $3$ .

$x^{4} = 244140625$

Step 3

Solve for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{244140625}$

Simplify $\pm \sqrt[4]{244140625}$ .

Rewrite $244140625$ as $125^{4}$ .

$x = \pm \sqrt[4]{125^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 125$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 125$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 125$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 125, - 125$