Simplify (3x^5)^2*2x^-3

${(3 x^{5})}^{2} \cdot 2 x^{- 3}$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(3 x^{5})}^{2} x^{- 3}$

Step 2

Apply the product rule to $3 x^{5}$ .

$2 (3^{2} {(x^{5})}^{2}) x^{- 3}$

Step 3

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

$2 (9 {(x^{5})}^{2}) x^{- 3}$

Step 4

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$2 (9 x^{5 \cdot 2}) x^{- 3}$

Multiply $5$ by $2$ .

$2 (9 x^{10}) x^{- 3}$

Step 5

Multiply $x^{10}$ by $x^{- 3}$ by adding the exponents.

Move $x^{- 3}$ .

$2 (9 (x^{- 3} x^{10}))$

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

$2 (9 x^{- 3 + 10})$

Add $- 3$ and $10$ .

$2 (9 x^{7})$

Step 6

Multiply $9$ by $2$ .

$18 x^{7}$