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Popular >

simplify e^{-y}(1+2^{-2x})

Solution

simplify

e^{- y} (1 + 2^{- 2 x})

Solution

\frac{4 ^{- x} + 1}{e ^{y}}

Solution steps

e^{- y} (1 + 2^{- 2 x})

Apply exponent rule:

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

= \frac{1}{e ^{y}} (2^{- 2 x} + 1)

Multiply fractions:

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

= \frac{1 \cdot ( 1 + 2 ^{- 2 x} )}{e ^{y}}

1 \cdot (1 + 2^{- 2 x}) = 1 + 2^{- 2 x}

= \frac{1 + 2 ^{- 2 x}}{e ^{y}}

2^{- 2 x} = 4^{- x}

= \frac{1 + 4 ^{- x}}{e ^{y}}

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Frequently Asked Questions (FAQ)

What is e^{-y}(1+2^{-2x}) ?
The solution to e^{-y}(1+2^{-2x}) is (4^{-x}+1)/(e^y)