Precalculus Examples

$\frac{e^{6}}{e^{- 1} + e^{- 2}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

$\frac{e^{6}}{\frac{1}{e} + e^{- 2}}$

Step 1.2

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

$\frac{e^{6}}{\frac{1}{e} + \frac{1}{e^{2}}}$

Step 1.3

To write $\frac{1}{e}$ as a fraction with a common denominator, multiply by $\frac{e}{e}$ .

$\frac{e^{6}}{\frac{1}{e} \cdot \frac{e}{e} + \frac{1}{e^{2}}}$

Step 1.4

Write each expression with a common denominator of $e^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{1}{e}$ by $\frac{e}{e}$ .

$\frac{e^{6}}{\frac{e}{e e} + \frac{1}{e^{2}}}$

Step 1.4.2

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

$\frac{e^{6}}{\frac{e}{e^{1} e} + \frac{1}{e^{2}}}$

Step 1.4.3

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

$\frac{e^{6}}{\frac{e}{e^{1} e^{1}} + \frac{1}{e^{2}}}$

Step 1.4.4

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

$\frac{e^{6}}{\frac{e}{e^{1 + 1}} + \frac{1}{e^{2}}}$

Step 1.4.5

Add $1$ and $1$ .

$\frac{e^{6}}{\frac{e}{e^{2}} + \frac{1}{e^{2}}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{e^{6}}{\frac{e + 1}{e^{2}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$e^{6} \frac{e^{2}}{e + 1}$

Step 3

Multiply $e^{6} \frac{e^{2}}{e + 1}$ .

Tap for more steps...

Step 3.1

Combine $e^{6}$ and $\frac{e^{2}}{e + 1}$ .

$\frac{e^{6} e^{2}}{e + 1}$

Step 3.2

Multiply $e^{6}$ by $e^{2}$ by adding the exponents.

Tap for more steps...

Step 3.2.1

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

$\frac{e^{6 + 2}}{e + 1}$

Step 3.2.2

Add $6$ and $2$ .

$\frac{e^{8}}{e + 1}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{8}}{e + 1}$

Decimal Form:

$801.70307807 \dots$