Algebra Examples

$4 r^{- 7} s^{- 1} \cdot 7 r^{- 2} s^{5} t^{0}$

Step 1

Multiply $r^{- 7}$ by $r^{- 2}$ by adding the exponents.

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Step 1.1

Move $r^{- 2}$ .

$4 (r^{- 2} r^{- 7}) s^{- 1} \cdot (7 s^{5} t^{0})$

Step 1.2

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

$4 r^{- 2 - 7} s^{- 1} \cdot (7 s^{5} t^{0})$

Step 1.3

Subtract $7$ from $- 2$ .

$4 r^{- 9} s^{- 1} \cdot (7 s^{5} t^{0})$

Step 2

Simplify $4 r^{- 9} s^{- 1} \cdot (7 s^{5} t^{0})$ .

$4 r^{- 9} s^{- 1} \cdot (7 s^{5})$

Step 3

Multiply $s^{- 1}$ by $s^{5}$ by adding the exponents.

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Step 3.1

Move $s^{5}$ .

$4 r^{- 9} (s^{5} s^{- 1}) \cdot 7$

Step 3.2

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

$4 r^{- 9} s^{5 - 1} \cdot 7$

Step 3.3

Subtract $1$ from $5$ .

$4 r^{- 9} s^{4} \cdot 7$

Step 4

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

$4 \frac{1}{r^{9}} s^{4} \cdot 7$

Step 5

Combine $4$ and $\frac{1}{r^{9}}$ .

$\frac{4}{r^{9}} s^{4} \cdot 7$

Step 6

Combine $\frac{4}{r^{9}}$ and $s^{4}$ .

$\frac{4 s^{4}}{r^{9}} \cdot 7$

Step 7

Multiply $\frac{4 s^{4}}{r^{9}} \cdot 7$ .

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Step 7.1

Combine $\frac{4 s^{4}}{r^{9}}$ and $7$ .

$\frac{4 s^{4} \cdot 7}{r^{9}}$

Step 7.2

Multiply $7$ by $4$ .

$\frac{28 s^{4}}{r^{9}}$