Solve for x 5^(2x)*5^(4x)=125

$5^{2 x} \cdot 5^{4 x} = 125$

Multiply $5^{2 x}$ by $5^{4 x}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5^{2 x + 4 x} = 125$

Add $2 x$ and $4 x$ .

$5^{6 x} = 125$

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

$5^{6 x} = 5^{3}$

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

$6 x = 3$

Divide each term in $6 x = 3$ by $6$ and simplify.

Divide each term in $6 x = 3$ by $6$ .

$\frac{6 x}{6} = \frac{3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{3}{6}$

Divide $x$ by $1$ .

$x = \frac{3}{6}$

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$