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Popular >

simplify 2^{x+1}+2^{x-1}

Solution

simplify

2^{x + 1} + 2^{x - 1}

Solution

5 \cdot 2^{x - 1}

Solution steps

2^{x + 1} + 2^{x - 1}

2^{x + 1} = 2^{x - 1 + 2}

= 2^{x - 1 + 2} + 2^{x - 1}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

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

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

Factor out common term

2^{x - 1}

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

Refine

= 5 \cdot 2^{x - 1}

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Frequently Asked Questions (FAQ)

What is 2^{x+1}+2^{x-1} ?
The solution to 2^{x+1}+2^{x-1} is 5*2^{x-1}