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Popular >

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

Solution

simplify

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

Solution

7 \cdot 2^{x - 2}

Solution steps

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

2^{x + 1} = 2^{x - 2 + 3}

= 2^{x - 2 + 3} - 2^{x - 2}

Apply exponent rule:

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

2^{x - 2 + 3} = 2^{3} \cdot 2^{x - 2}

= 2^{3} \cdot 2^{x - 2} - 2^{x - 2}

Factor out common term

2^{x - 2}

= 2^{x - 2} (2^{3} - 1)

Refine

= 7 \cdot 2^{x - 2}

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Frequently Asked Questions (FAQ)

What is 2^{x+1}-2^{x-2} ?
The solution to 2^{x+1}-2^{x-2} is 7*2^{x-2}