Basic Math Examples

$5 e^{- 8} \cdot {(- 2 e^{3})}^{2}$

Step 1

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

$5 \frac{1}{e^{8}} \cdot {(- 2 e^{3})}^{2}$

Step 2

Combine $5$ and $\frac{1}{e^{8}}$ .

$\frac{5}{e^{8}} \cdot {(- 2 e^{3})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $- 2 e^{3}$ .

$\frac{5}{e^{8}} \cdot ({(- 2)}^{2} {(e^{3})}^{2})$

Step 3.2

Raise $- 2$ to the power of $2$ .

$\frac{5}{e^{8}} \cdot (4 {(e^{3})}^{2})$

Step 3.3

Multiply the exponents in ${(e^{3})}^{2}$ .

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Step 3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5}{e^{8}} \cdot (4 e^{3 \cdot 2})$

Step 3.3.2

Multiply $3$ by $2$ .

$\frac{5}{e^{8}} \cdot (4 e^{6})$

Step 4

Cancel the common factor of $e^{6}$ .

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Step 4.1

Factor $e^{6}$ out of $e^{8}$ .

$\frac{5}{e^{6} e^{2}} \cdot (4 e^{6})$

Step 4.2

Factor $e^{6}$ out of $4 e^{6}$ .

$\frac{5}{e^{6} e^{2}} \cdot (e^{6} \cdot 4)$

Step 4.3

Cancel the common factor.

$\frac{5}{e^{6} e^{2}} \cdot (e^{6} \cdot 4)$

Step 4.4

Rewrite the expression.

$\frac{5}{e^{2}} \cdot 4$

Step 5

Combine $\frac{5}{e^{2}}$ and $4$ .

$\frac{5 \cdot 4}{e^{2}}$

Step 6

Multiply $5$ by $4$ .

$\frac{20}{e^{2}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{20}{e^{2}}$

Decimal Form:

$2.70670566 \dots$