Simplify (4^5*4^10)/(4^6)

$\frac{4^{5} \cdot 4^{10}}{4^{6}}$

Multiply $4^{5}$ by $4^{10}$ by adding the exponents.

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

$\frac{4^{5 + 10}}{4^{6}}$

Add $5$ and $10$ .

$\frac{4^{15}}{4^{6}}$

Cancel the common factor of $4^{15}$ and $4^{6}$ .

Factor $4^{6}$ out of $4^{15}$ .

$\frac{4^{6} \cdot 4^{9}}{4^{6}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{4^{6} \cdot 4^{9}}{4^{6} \cdot 1}$

Cancel the common factor.

$\frac{4^{6} \cdot 4^{9}}{4^{6} \cdot 1}$

Rewrite the expression.

$\frac{4^{9}}{1}$

Divide $4^{9}$ by $1$ .

$4^{9}$

Raise $4$ to the power of $9$ .

$262144$