Simplify (8x^3)^2(2x^2)^3

${(8 x^{3})}^{2} {(2 x^{2})}^{3}$

Step 1

Apply the product rule to $8 x^{3}$ .

$8^{2} {(x^{3})}^{2} {(2 x^{2})}^{3}$

Step 2

Raise $8$ to the power of $2$ .

$64 {(x^{3})}^{2} {(2 x^{2})}^{3}$

Step 3

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

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

$64 x^{3 \cdot 2} {(2 x^{2})}^{3}$

Multiply $3$ by $2$ .

$64 x^{6} {(2 x^{2})}^{3}$

Step 4

Apply the product rule to $2 x^{2}$ .

$64 x^{6} (2^{3} {(x^{2})}^{3})$

Step 5

Rewrite using the commutative property of multiplication.

$64 \cdot 2^{3} x^{6} {(x^{2})}^{3}$

Step 6

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

$64 \cdot 8 x^{6} {(x^{2})}^{3}$

Step 7

Multiply $64$ by $8$ .

$512 x^{6} {(x^{2})}^{3}$

Step 8

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

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

$512 x^{6} x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$512 x^{6} x^{6}$

Step 9

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

Move $x^{6}$ .

$512 (x^{6} x^{6})$

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

$512 x^{6 + 6}$

Add $6$ and $6$ .

$512 x^{12}$