Simplify 5(x^3)^-3(2x)^-4

$5 {(x^{3})}^{- 3} {(2 x)}^{- 4}$

Step 1

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

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

$5 x^{3 \cdot - 3} {(2 x)}^{- 4}$

Multiply $3$ by $- 3$ .

$5 x^{- 9} {(2 x)}^{- 4}$

Step 2

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

$5 \frac{1}{x^{9}} {(2 x)}^{- 4}$

Step 3

Combine $5$ and $\frac{1}{x^{9}}$ .

$\frac{5}{x^{9}} {(2 x)}^{- 4}$

Step 4

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

$\frac{5}{x^{9}} \cdot \frac{1}{{(2 x)}^{4}}$

Step 5

Combine fractions.

Combine.

$\frac{5 \cdot 1}{x^{9} {(2 x)}^{4}}$

Multiply $5$ by $1$ .

$\frac{5}{x^{9} {(2 x)}^{4}}$

Step 6

Simplify the denominator.

Apply the product rule to $2 x$ .

$\frac{5}{x^{9} \cdot 2^{4} x^{4}}$

Multiply $x^{9}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{5}{x^{4} x^{9} \cdot 2^{4}}$

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

$\frac{5}{x^{4 + 9} \cdot 2^{4}}$

Add $4$ and $9$ .

$\frac{5}{x^{13} \cdot 2^{4}}$

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

$\frac{5}{x^{13} \cdot 16}$

Step 7

Move $16$ to the left of $x^{13}$ .

$\frac{5}{16 x^{13}}$