Solve for z 2^(3z+9)=8^(2z+1)

$2^{3 z + 9} = 8^{2 z + 1}$

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

$2^{3 z + 9} = 2^{3 (2 z + 1)}$

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

$3 z + 9 = 3 (2 z + 1)$

Solve for $z$ .

Simplify $3 (2 z + 1)$ .

Rewrite.

$3 z + 9 = 0 + 0 + 3 (2 z + 1)$

Simplify by adding zeros.

$3 z + 9 = 3 (2 z + 1)$

Apply the distributive property.

$3 z + 9 = 3 (2 z) + 3 \cdot 1$

Multiply.

Multiply $2$ by $3$ .

$3 z + 9 = 6 z + 3 \cdot 1$

Multiply $3$ by $1$ .

$3 z + 9 = 6 z + 3$

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

Subtract $6 z$ from both sides of the equation.

$3 z + 9 - 6 z = 3$

Subtract $6 z$ from $3 z$ .

$- 3 z + 9 = 3$

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

Subtract $9$ from both sides of the equation.

$- 3 z = 3 - 9$

Subtract $9$ from $3$ .

$- 3 z = - 6$

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

Divide each term in $- 3 z = - 6$ by $- 3$ .

$\frac{- 3 z}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 z}{- 3} = \frac{- 6}{- 3}$

Divide $z$ by $1$ .

$z = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$z = 2$