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Popular >

simplify (2^{-x})/(2^x)

Solution

simplify

\frac{2 ^{- x}}{2 ^{x}}

Solution

\frac{1}{4 ^{x}}

Solution steps

\frac{2 ^{- x}}{2 ^{x}}

Apply exponent rule:

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

= 2^{- x - x}

Add similar elements:

- x - x = - 2 x

= 2^{- 2 x}

Apply exponent rule:

a^{b x} = (a^{b})^{x}

2^{- 2 x} = (2^{2})^{- x}

= (2^{2})^{- x}

2^{2} = 4

= 4^{- x}

Apply exponent rule:

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

4^{- x} = \frac{1}{4 ^{x}}

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

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Frequently Asked Questions (FAQ)

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