Precalculus Examples

${(2 r^{- 1})}^{4} {(4 r^{2})}^{- 2}$

Step 1

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

${(2 \frac{1}{r})}^{4} {(4 r^{2})}^{- 2}$

Step 2

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

${(\frac{2}{r})}^{4} {(4 r^{2})}^{- 2}$

Step 3

Simplify the expression.

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Step 3.1

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

$\frac{2^{4}}{r^{4}} {(4 r^{2})}^{- 2}$

Step 3.2

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

$\frac{16}{r^{4}} {(4 r^{2})}^{- 2}$

Step 4

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

$\frac{16}{r^{4}} \cdot \frac{1}{{(4 r^{2})}^{2}}$

Step 5

Combine fractions.

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Step 5.1

Combine.

$\frac{16 \cdot 1}{r^{4} {(4 r^{2})}^{2}}$

Step 5.2

Multiply $16$ by $1$ .

$\frac{16}{r^{4} {(4 r^{2})}^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Apply the product rule to $4 r^{2}$ .

$\frac{16}{r^{4} \cdot 4^{2} {(r^{2})}^{2}}$

Step 6.2

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

$\frac{16}{r^{4} \cdot 16 {(r^{2})}^{2}}$

Step 6.3

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

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Step 6.3.1

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

$\frac{16}{r^{4} \cdot 16 r^{2 \cdot 2}}$

Step 6.3.2

Multiply $2$ by $2$ .

$\frac{16}{r^{4} \cdot 16 r^{4}}$

Step 6.4

Multiply $r^{4}$ by $r^{4}$ by adding the exponents.

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Step 6.4.1

Move $r^{4}$ .

$\frac{16}{r^{4} r^{4} \cdot 16}$

Step 6.4.2

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

$\frac{16}{r^{4 + 4} \cdot 16}$

Step 6.4.3

Add $4$ and $4$ .

$\frac{16}{r^{8} \cdot 16}$

Step 7

Cancel the common factor of $16$ .

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Step 7.1

Cancel the common factor.

$\frac{16}{r^{8} \cdot 16}$

Step 7.2

Rewrite the expression.

$\frac{1}{r^{8}}$