Algebra Examples

$\frac{1}{2} e^{- 2} {(2 e^{4})}^{3}$

Step 1

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

$\frac{1}{2} \cdot (\frac{1}{e^{2}} {(2 e^{4})}^{3})$

Step 2

Simplify terms.

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Step 2.1

Apply the product rule to $2 e^{4}$ .

$\frac{1}{2} \cdot (\frac{1}{e^{2}} (2^{3} {(e^{4})}^{3}))$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $\frac{1}{e^{2}} (2^{3} {(e^{4})}^{3})$ .

$\frac{1}{2} \cdot (2 (\frac{1}{e^{2}} (2^{2} {(e^{4})}^{3})))$

Step 2.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (\frac{1}{e^{2}} (2^{2} {(e^{4})}^{3})))$

Step 2.2.3

Rewrite the expression.

$\frac{1}{e^{2}} (2^{2} {(e^{4})}^{3})$

Step 2.3

Combine $2^{2}$ and $\frac{1}{e^{2}}$ .

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

Step 2.4

Combine $\frac{2^{2}}{e^{2}}$ and ${(e^{4})}^{3}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Multiply the exponents in ${(e^{4})}^{3}$ .

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Step 3.2.1

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

$\frac{4 e^{4 \cdot 3}}{e^{2}}$

Step 3.2.2

Multiply $4$ by $3$ .

$\frac{4 e^{12}}{e^{2}}$

Step 4

Cancel the common factor of $e^{12}$ and $e^{2}$ .

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Step 4.1

Factor $e^{2}$ out of $4 e^{12}$ .

$\frac{e^{2} (4 e^{10})}{e^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{e^{2} (4 e^{10})}{e^{2} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{e^{2} (4 e^{10})}{e^{2} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{4 e^{10}}{1}$

Step 4.2.4

Divide $4 e^{10}$ by $1$ .

$4 e^{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$4 e^{10}$

Decimal Form:

$88105.86317922 \dots$