Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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.

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Step 5.1

Combine.

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

Step 5.2

Multiply $5$ by $1$ .

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

Step 6

Simplify the denominator.

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Step 6.1

Apply the product rule to $2 x$ .

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

Step 6.2

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

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Step 6.2.1

Move $x^{4}$ .

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

Step 6.2.2

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

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

Step 6.2.3

Add $4$ and $9$ .

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

Step 6.3

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

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

Step 7

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

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