Solve for x 625*5^(3x+3)=125

$625 \cdot 5^{3 x + 3} = 125$

Rewrite $625$ as $5^{4}$ .

$5^{4} \cdot 5^{3 x + 3} = 125$

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

$5^{4 + 3 x + 3} = 125$

Add $4$ and $3$ .

$5^{3 x + 7} = 125$

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

$5^{3 x + 7} = 5^{3}$

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

$3 x + 7 = 3$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$3 x = 3 - 7$

Subtract $7$ from $3$ .

$3 x = - 4$

Divide each term in $3 x = - 4$ by $3$ and simplify.

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$