What is e^{-2x^7}x^{-8} ?

The solution to e^{-2x^7}x^{-8} is 1/(e^{2x^7)x^8}

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simplify e^{-2x^7}x^{-8}

simplify

e^{- 2 x^{7}} x^{- 8}

\frac{1}{e ^{2 x^{7}} x ^{8}}

Solution steps

e^{- 2 x^{7}} x^{- 8}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2 x^{7}}} x^{- 8}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2 x^{7}}} \cdot \frac{1}{x ^{8}}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{e ^{2 x^{7}} x ^{8}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{e ^{2 x^{7}} x ^{8}}

(e^{\frac{h v}{k T}} - 1)^{- 1}

(\frac{2}{9}) e^{- 1}

x^{- \frac{5}{2} = 32}