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Popular >

simplify (e^{4x})/4*e^{-x}

Solution

simplify

\frac{e ^{4 x}}{4} \cdot e^{- x}

Solution

\frac{e ^{3 x}}{4}

Solution steps

\frac{e ^{4 x}}{4} e^{- x}

Apply exponent rule:

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

= \frac{e ^{4 x}}{4} \cdot \frac{1}{e ^{x}}

Multiply fractions:

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

= \frac{e ^{4 x} \cdot 1}{4 e ^{x}}

Multiply:

e^{4 x} \cdot 1 = e^{4 x}

= \frac{e ^{4 x}}{4 e ^{x}}

Apply exponent rule:

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

\frac{e ^{4 x}}{e ^{x}} = e^{4 x - x} = e^{3 x}

= \frac{e ^{3 x}}{4}

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Frequently Asked Questions (FAQ)

What is (e^{4x})/4*e^{-x} ?
The solution to (e^{4x})/4*e^{-x} is (e^{3x})/4