Basic Math Examples

$5 e^{2} (- 3 e^{2} - 2 e - 3)$

Step 1

Apply the distributive property.

$5 e^{2} (- 3 e^{2}) + 5 e^{2} (- 2 e) + 5 e^{2} \cdot - 3$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $e^{2}$ .

$5 (e^{2} e^{2}) \cdot - 3 + 5 e^{2} (- 2 e) + 5 e^{2} \cdot - 3$

Step 2.1.2

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

$5 e^{2 + 2} \cdot - 3 + 5 e^{2} (- 2 e) + 5 e^{2} \cdot - 3$

Step 2.1.3

Add $2$ and $2$ .

$5 e^{4} \cdot - 3 + 5 e^{2} (- 2 e) + 5 e^{2} \cdot - 3$

Step 2.2

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

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Step 2.2.1

Move $e$ .

$5 e^{4} \cdot - 3 + 5 (e e^{2}) \cdot - 2 + 5 e^{2} \cdot - 3$

Step 2.2.2

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

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Step 2.2.2.1

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

$5 e^{4} \cdot - 3 + 5 (e^{1} e^{2}) \cdot - 2 + 5 e^{2} \cdot - 3$

Step 2.2.2.2

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

$5 e^{4} \cdot - 3 + 5 e^{1 + 2} \cdot - 2 + 5 e^{2} \cdot - 3$

Step 2.2.3

Add $1$ and $2$ .

$5 e^{4} \cdot - 3 + 5 e^{3} \cdot - 2 + 5 e^{2} \cdot - 3$

Step 2.3

Multiply $- 3$ by $5$ .

$5 e^{4} \cdot - 3 + 5 e^{3} \cdot - 2 - 15 e^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 3$ by $5$ .

$- 15 e^{4} + 5 e^{3} \cdot - 2 - 15 e^{2}$

Step 3.2

Multiply $- 2$ by $5$ .

$- 15 e^{4} - 10 e^{3} - 15 e^{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 15 e^{4} - 10 e^{3} - 15 e^{2}$

Decimal Form:

$- 1130.66346121 \dots$