Solve for x 5^(3x) = cube root of 25

$5^{3 x} = \sqrt[3]{25}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{25}$ as $25^{\frac{1}{3}}$ .

$5^{3 x} = 25^{\frac{1}{3}}$

Create equivalent expressions in the equation that all have equal bases.

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

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$3 x = 2 (\frac{1}{3})$

Solve for $x$ .

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

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

Divide each term in $3 x = \frac{2}{3}$ by $3$ and simplify.

Divide each term in $3 x = \frac{2}{3}$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{2}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{2}{3}$ by $\frac{1}{3}$ .

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

Multiply $3$ by $3$ .

$x = \frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{9}$

Decimal Form:

$x = 0.\overline{2}$