Algebra Examples

$(4 d^{2} t^{5} v^{- 4}) (- 5 d t^{- 3} v^{- 1})$

Step 1

Multiply $d^{2}$ by $d$ by adding the exponents.

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Step 1.1

Move $d$ .

$4 (d \cdot d^{2}) t^{5} v^{- 4} (- 5 t^{- 3} v^{- 1})$

Step 1.2

Multiply $d$ by $d^{2}$ .

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Step 1.2.1

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

$4 (d^{1} d^{2}) t^{5} v^{- 4} (- 5 t^{- 3} v^{- 1})$

Step 1.2.2

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

$4 d^{1 + 2} t^{5} v^{- 4} (- 5 t^{- 3} v^{- 1})$

Step 1.3

Add $1$ and $2$ .

$4 d^{3} t^{5} v^{- 4} (- 5 t^{- 3} v^{- 1})$

Step 2

Multiply $t^{5}$ by $t^{- 3}$ by adding the exponents.

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Step 2.1

Move $t^{- 3}$ .

$4 d^{3} (t^{- 3} t^{5}) v^{- 4} (- 5 v^{- 1})$

Step 2.2

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

$4 d^{3} t^{- 3 + 5} v^{- 4} (- 5 v^{- 1})$

Step 2.3

Add $- 3$ and $5$ .

$4 d^{3} t^{2} v^{- 4} (- 5 v^{- 1})$

Step 3

Multiply $v^{- 4}$ by $v^{- 1}$ by adding the exponents.

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Step 3.1

Move $v^{- 1}$ .

$4 d^{3} t^{2} (v^{- 1} v^{- 4}) \cdot - 5$

Step 3.2

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

$4 d^{3} t^{2} v^{- 1 - 4} \cdot - 5$

Step 3.3

Subtract $4$ from $- 1$ .

$4 d^{3} t^{2} v^{- 5} \cdot - 5$

Step 4

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

$4 d^{3} t^{2} \frac{1}{v^{5}} \cdot - 5$

Step 5

Multiply $4 d^{3} t^{2} \frac{1}{v^{5}}$ .

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Step 5.1

Combine $4$ and $\frac{1}{v^{5}}$ .

$d^{3} t^{2} \frac{4}{v^{5}} \cdot - 5$

Step 5.2

Combine $d^{3}$ and $\frac{4}{v^{5}}$ .

$t^{2} \frac{d^{3} \cdot 4}{v^{5}} \cdot - 5$

Step 5.3

Combine $t^{2}$ and $\frac{d^{3} \cdot 4}{v^{5}}$ .

$\frac{t^{2} (d^{3} \cdot 4)}{v^{5}} \cdot - 5$

Step 6

Move $4$ to the left of $t^{2} d^{3}$ .

$\frac{4 \cdot (t^{2} d^{3})}{v^{5}} \cdot - 5$

Step 7

Multiply $\frac{4 t^{2} d^{3}}{v^{5}} \cdot - 5$ .

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Step 7.1

Combine $\frac{4 t^{2} d^{3}}{v^{5}}$ and $- 5$ .

$\frac{4 t^{2} d^{3} \cdot - 5}{v^{5}}$

Step 7.2

Multiply $- 5$ by $4$ .

$\frac{- 20 t^{2} d^{3}}{v^{5}}$

Step 8

Move the negative in front of the fraction.

$- \frac{20 t^{2} d^{3}}{v^{5}}$