Evaluate 216^x=6^(x+10)

$216^{x} = 6^{x + 10}$

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

$6^{3 x} = 6^{x + 10}$

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

$3 x = x + 10$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 x - x = 10$

Subtract $x$ from $3 x$ .

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$