Simplify (2x^2)(x^2)^6(3x^2)^3

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

Step 1

Multiply the exponents in ${(x^{2})}^{6}$ .

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

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

Multiply $2$ by $6$ .

$2 x^{2} x^{12} {(3 x^{2})}^{3}$

Step 2

Multiply $x^{2}$ by $x^{12}$ by adding the exponents.

Move $x^{12}$ .

$2 (x^{12} x^{2}) {(3 x^{2})}^{3}$

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

$2 x^{12 + 2} {(3 x^{2})}^{3}$

Add $12$ and $2$ .

$2 x^{14} {(3 x^{2})}^{3}$

Step 3

Apply the product rule to $3 x^{2}$ .

$2 x^{14} (3^{3} {(x^{2})}^{3})$

Step 4

Rewrite using the commutative property of multiplication.

$2 \cdot 3^{3} x^{14} {(x^{2})}^{3}$

Step 5

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

$2 \cdot 27 x^{14} {(x^{2})}^{3}$

Step 6

Multiply $2$ by $27$ .

$54 x^{14} {(x^{2})}^{3}$

Step 7

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

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

$54 x^{14} x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$54 x^{14} x^{6}$

Step 8

Multiply $x^{14}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$54 (x^{6} x^{14})$

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

$54 x^{6 + 14}$

Add $6$ and $14$ .

$54 x^{20}$