Evaluate (3/2x^-7)(2x^-1)^5

$(\frac{3}{2} x^{- 7}) {(2 x^{- 1})}^{5}$

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

$\frac{3}{2} \cdot \frac{1}{x^{7}} {(2 x^{- 1})}^{5}$

Combine.

$\frac{3 \cdot 1}{2 x^{7}} {(2 x^{- 1})}^{5}$

Multiply $3$ by $1$ .

$\frac{3}{2 x^{7}} {(2 x^{- 1})}^{5}$

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

$\frac{3}{2 x^{7}} {(2 \frac{1}{x})}^{5}$

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

$\frac{3}{2 x^{7}} {(\frac{2}{x})}^{5}$

Apply the product rule to $\frac{2}{x}$ .

$\frac{3}{2 x^{7}} \cdot \frac{2^{5}}{x^{5}}$

Combine.

$\frac{3 \cdot 2^{5}}{2 x^{7} x^{5}}$

Multiply $x^{7}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{3 \cdot 2^{5}}{2 (x^{5} x^{7})}$

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

$\frac{3 \cdot 2^{5}}{2 x^{5 + 7}}$

Add $5$ and $7$ .

$\frac{3 \cdot 2^{5}}{2 x^{12}}$

Cancel the common factor of $2^{5}$ and $2$ .

Factor $2$ out of $3 \cdot 2^{5}$ .

$\frac{2 (3 \cdot 2^{4})}{2 x^{12}}$

Cancel the common factors.

Factor $2$ out of $2 x^{12}$ .

$\frac{2 (3 \cdot 2^{4})}{2 (x^{12})}$

Cancel the common factor.

$\frac{2 (3 \cdot 2^{4})}{2 x^{12}}$

Rewrite the expression.

$\frac{3 \cdot 2^{4}}{x^{12}}$

Simplify the expression.

Raise $2$ to the power of $4$ .

$\frac{3 \cdot 16}{x^{12}}$

Multiply $3$ by $16$ .

$\frac{48}{x^{12}}$