Evaluate (4^9)/(4^3*4^4)

$\frac{4^{9}}{4^{3} \cdot 4^{4}}$

Multiply $4^{3}$ by $4^{4}$ by adding the exponents.

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

$\frac{4^{9}}{4^{3 + 4}}$

Add $3$ and $4$ .

$\frac{4^{9}}{4^{7}}$

Cancel the common factor of $4^{9}$ and $4^{7}$ .

Factor $4^{7}$ out of $4^{9}$ .

$\frac{4^{7} \cdot 4^{2}}{4^{7}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{4^{7} \cdot 4^{2}}{4^{7} \cdot 1}$

Cancel the common factor.

$\frac{4^{7} \cdot 4^{2}}{4^{7} \cdot 1}$

Rewrite the expression.

$\frac{4^{2}}{1}$

Divide $4^{2}$ by $1$ .

$4^{2}$

Raise $4$ to the power of $2$ .

$16$