Basic Math Examples

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

Step 1

Multiply $r^{- 1}$ by $r$ by adding the exponents.

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Step 1.1

Multiply $r^{- 1}$ by $r$ .

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Step 1.1.1

Raise $r$ to the power of $1$ .

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

Step 1.1.2

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

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

Step 1.2

Add $- 1$ and $1$ .

$\frac{{(2 r)}^{- 4}}{r^{0}}$

Step 2

Simplify the expression.

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Step 2.1

Simplify $r^{0}$ .

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

Step 2.2

Move ${(2 r)}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $2 r$ .

$\frac{1}{2^{4} r^{4}}$

Step 3.2

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

$\frac{1}{16 r^{4}}$