Solve for n 4^3*4^n=4^9

$4^{3} \cdot 4^{n} = 4^{9}$

Step 1

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

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

Step 2

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

$3 + n = 9$

Step 3

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

Subtract $3$ from both sides of the equation.

$n = 9 - 3$

Subtract $3$ from $9$ .

$n = 6$