Basic Math Examples

$\frac{4}{5} \cdot \frac{d i v i d e \cdot 1}{10}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{4}{5} \cdot \frac{d^{1} d i v i e \cdot 1}{10}$

Step 1.2

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

$\frac{4}{5} \cdot \frac{d^{1} d^{1} i v i e \cdot 1}{10}$

Step 1.3

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

$\frac{4}{5} \cdot \frac{d^{1 + 1} i v i e \cdot 1}{10}$

Step 1.4

Add $1$ and $1$ .

$\frac{4}{5} \cdot \frac{d^{2} i v i e \cdot 1}{10}$

Step 1.5

Multiply $d^{2}$ by $1$ .

$\frac{4}{5} \cdot \frac{d^{2} i v i e}{10}$

Step 1.6

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

$\frac{4}{5} \cdot \frac{d^{2} v (i^{1} i) e}{10}$

Step 1.7

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

$\frac{4}{5} \cdot \frac{d^{2} v (i^{1} i^{1}) e}{10}$

Step 1.8

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

$\frac{4}{5} \cdot \frac{d^{2} v i^{1 + 1} e}{10}$

Step 1.9

Add $1$ and $1$ .

$\frac{4}{5} \cdot \frac{d^{2} v i^{2} e}{10}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $i^{2}$ as $- 1$ .

$\frac{4}{5} \cdot \frac{d^{2} v \cdot - 1 e}{10}$

Step 2.2

Factor out negative.

$\frac{4}{5} \cdot \frac{- d^{2} v e}{10}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{4 (- d^{2} v e)}{5 \cdot 10}$

Step 3.2

Cancel the common factor of $4$ and $10$ .

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Step 3.2.1

Factor $2$ out of $4 (- d^{2} v e)$ .

$\frac{2 (2 (- d^{2} v e))}{5 \cdot 10}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $5 \cdot 10$ .

$\frac{2 (2 (- d^{2} v e))}{2 (5 \cdot 5)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 (2 (- d^{2} v e))}{2 (5 \cdot 5)}$

Step 3.2.2.3

Rewrite the expression.

$\frac{2 (- d^{2} v e)}{5 \cdot 5}$

Step 3.3

Multiply.

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Step 3.3.1

Multiply $- 1$ by $2$ .

$\frac{- 2 (d^{2} v e)}{5 \cdot 5}$

Step 3.3.2

Multiply $5$ by $5$ .

$\frac{- 2 (d^{2} v e)}{25}$

Step 4

Remove parentheses.

$\frac{- 2 d^{2} v e}{25}$

Step 5

Move the negative in front of the fraction.

$- \frac{2 d^{2} v e}{25}$