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

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Multiply $x^{- 3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

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

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

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

Subtract $3$ from $5$ .

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

Step 3

Apply the product rule to $- 3 x$ .

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

Step 4

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 5

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

$3 (9 x^{4})$

Step 6

Multiply $9$ by $3$ .

$27 x^{4}$