Simplify (3x^2)^3(2x)^-1

${(3 x^{2})}^{3} {(2 x)}^{- 1}$

Step 1

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

$3^{3} {(x^{2})}^{3} {(2 x)}^{- 1}$

Step 2

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

$27 {(x^{2})}^{3} {(2 x)}^{- 1}$

Step 3

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

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

$27 x^{2 \cdot 3} {(2 x)}^{- 1}$

Multiply $2$ by $3$ .

$27 x^{6} {(2 x)}^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$27 x^{6} \frac{1}{2 x}$

Step 5

Cancel the common factor of $x$ .

Factor $x$ out of $27 x^{6}$ .

$x (27 x^{5}) \frac{1}{2 x}$

Factor $x$ out of $2 x$ .

$x (27 x^{5}) \frac{1}{x \cdot 2}$

Cancel the common factor.

$x (27 x^{5}) \frac{1}{x \cdot 2}$

Rewrite the expression.

$27 x^{5} \frac{1}{2}$

Step 6

Combine $27$ and $\frac{1}{2}$ .

$x^{5} \frac{27}{2}$

Step 7

Combine $x^{5}$ and $\frac{27}{2}$ .

$\frac{x^{5} \cdot 27}{2}$

Step 8

Move $27$ to the left of $x^{5}$ .

$\frac{27 x^{5}}{2}$