Calculus Examples

${(e^{- 6})}^{\frac{5}{6}}$

Step 1

Multiply the exponents in ${(e^{- 6})}^{\frac{5}{6}}$ .

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Step 1.1

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

$e^{- 6 (\frac{5}{6})}$

Step 1.2

Cancel the common factor of $6$ .

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Step 1.2.1

Factor $6$ out of $- 6$ .

$e^{6 (- 1) \frac{5}{6}}$

Step 1.2.2

Cancel the common factor.

$e^{6 \cdot - 1 \frac{5}{6}}$

Step 1.2.3

Rewrite the expression.

$e^{- 1 \cdot 5}$

Step 1.3

Multiply $- 1$ by $5$ .

$e^{- 5}$

Step 2

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

$\frac{1}{e^{5}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{e^{5}}$

Decimal Form:

$0.00673794 \dots$