Evaluate 7^(3y-8)=7^13

$7^{3 y - 8} = 7^{13}$

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

$7^{3 y - 8} = 7^{13}$

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

$3 y - 8 = 13$

Solve for $y$ .

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

Add $8$ to both sides of the equation.

$3 y = 13 + 8$

Add $13$ and $8$ .

$3 y = 21$

Divide each term in $3 y = 21$ by $3$ and simplify.

Divide each term in $3 y = 21$ by $3$ .

$\frac{3 y}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{21}{3}$

Divide $y$ by $1$ .

$y = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$y = 7$