Finite Math Examples

$- 5 r^{- 2} {(r^{- 5})}^{- 5}$

Step 1

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

$- 5 \frac{1}{r^{2}} {(r^{- 5})}^{- 5}$

Step 2

Combine $- 5$ and $\frac{1}{r^{2}}$ .

$\frac{- 5}{r^{2}} {(r^{- 5})}^{- 5}$

Step 3

Simplify the expression.

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Step 3.1

Move the negative in front of the fraction.

$- \frac{5}{r^{2}} {(r^{- 5})}^{- 5}$

Step 3.2

Multiply the exponents in ${(r^{- 5})}^{- 5}$ .

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Step 3.2.1

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

$- \frac{5}{r^{2}} r^{- 5 \cdot - 5}$

Step 3.2.2

Multiply $- 5$ by $- 5$ .

$- \frac{5}{r^{2}} r^{25}$

Step 4

Cancel the common factor of $r^{2}$ .

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Step 4.1

Move the leading negative in $- \frac{5}{r^{2}}$ into the numerator.

$\frac{- 5}{r^{2}} r^{25}$

Step 4.2

Factor $r^{2}$ out of $r^{25}$ .

$\frac{- 5}{r^{2}} (r^{2} r^{23})$

Step 4.3

Cancel the common factor.

$\frac{- 5}{r^{2}} (r^{2} r^{23})$

Step 4.4

Rewrite the expression.

$- 5 r^{23}$