Solve for y 16^(3y)=64^(y+9)

$16^{3 y} = 64^{y + 9}$

Step 1

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

$4^{2 (3 y)} = 4^{3 (y + 9)}$

Step 2

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

$2 (3 y) = 3 (y + 9)$

Step 3

Solve for $y$ .

Multiply $3$ by $2$ .

$6 y = 3 (y + 9)$

Simplify $3 (y + 9)$ .

Apply the distributive property.

$6 y = 3 y + 3 \cdot 9$

Multiply $3$ by $9$ .

$6 y = 3 y + 27$

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

Subtract $3 y$ from both sides of the equation.

$6 y - 3 y = 27$

Subtract $3 y$ from $6 y$ .

$3 y = 27$

Divide each term in $3 y = 27$ by $3$ and simplify.

Divide each term in $3 y = 27$ by $3$ .

$\frac{3 y}{3} = \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{27}{3}$

Divide $y$ by $1$ .

$y = \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$y = 9$