Simplify (x^9(2x)^4)/(x^3)

$\frac{x^{9} {(2 x)}^{4}}{x^{3}}$

Cancel the common factor of $x^{9}$ and $x^{3}$ .

Factor $x^{3}$ out of $x^{9} {(2 x)}^{4}$ .

$\frac{x^{3} (x^{6} {(2 x)}^{4})}{x^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{3} (x^{6} {(2 x)}^{4})}{x^{3} \cdot 1}$

Cancel the common factor.

$\frac{x^{3} (x^{6} {(2 x)}^{4})}{x^{3} \cdot 1}$

Rewrite the expression.

$\frac{x^{6} {(2 x)}^{4}}{1}$

Divide $x^{6} {(2 x)}^{4}$ by $1$ .

$x^{6} {(2 x)}^{4}$

Simplify the expression.

Apply the product rule to $2 x$ .

$x^{6} (2^{4} x^{4})$

Rewrite using the commutative property of multiplication.

$2^{4} x^{6} x^{4}$

Multiply $x^{6}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$2^{4} (x^{4} x^{6})$

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

$2^{4} x^{4 + 6}$

Add $4$ and $6$ .

$2^{4} x^{10}$

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

$16 x^{10}$