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

${(2 x)}^{4} {(3 x^{3})}^{2}$

Step 1

Apply the product rule to $2 x$ .

$2^{4} x^{4} {(3 x^{3})}^{2}$

Step 2

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

$16 x^{4} {(3 x^{3})}^{2}$

Step 3

Apply the product rule to $3 x^{3}$ .

$16 x^{4} (3^{2} {(x^{3})}^{2})$

Step 4

Rewrite using the commutative property of multiplication.

$16 \cdot 3^{2} x^{4} {(x^{3})}^{2}$

Step 5

Raise $3$ to the power of $2$ .

$16 \cdot 9 x^{4} {(x^{3})}^{2}$

Step 6

Multiply $16$ by $9$ .

$144 x^{4} {(x^{3})}^{2}$

Step 7

Multiply the exponents in ${(x^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$144 x^{4} x^{3 \cdot 2}$

Multiply $3$ by $2$ .

$144 x^{4} x^{6}$

Step 8

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

Move $x^{6}$ .

$144 (x^{6} x^{4})$

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

$144 x^{6 + 4}$

Add $6$ and $4$ .

$144 x^{10}$