Solve for n 4^n*4^(2n-9)=64

$4^{n} \cdot 4^{2 n - 9} = 64$

Step 1

Multiply $4^{n}$ by $4^{2 n - 9}$ by adding the exponents.

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

$4^{n + 2 n - 9} = 64$

Add $n$ and $2 n$ .

$4^{3 n - 9} = 64$

Step 2

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

$4^{3 n - 9} = 4^{3}$

Step 3

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

$3 n - 9 = 3$

Step 4

Solve for $n$ .

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

Add $9$ to both sides of the equation.

$3 n = 3 + 9$

Add $3$ and $9$ .

$3 n = 12$

Divide each term in $3 n = 12$ by $3$ and simplify.

Divide each term in $3 n = 12$ by $3$ .

$\frac{3 n}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} = \frac{12}{3}$

Divide $n$ by $1$ .

$n = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$n = 4$