Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine $d^{2}$ and $\frac{4}{v^{4}}$ .

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

Step 2.2.3

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

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

Step 2.3

Move $4$ to the left of $t^{5} d^{2}$ .

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

Step 2.4

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

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

Step 2.5

Multiply $- 5 d \frac{1}{t^{3}}$ .

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Step 2.5.1

Combine $- 5$ and $\frac{1}{t^{3}}$ .

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

Step 2.5.2

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

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

Step 2.6

Move $- 5$ to the left of $d$ .

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

Step 2.7

Move the negative in front of the fraction.

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

Step 2.8

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

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

Step 2.9

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

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