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Popular >

simplify 2^{x+3}-2^{x+4}

Solution

simplify

2^{x + 3} - 2^{x + 4}

Solution

- 2^{x + 3}

Solution steps

2^{x + 3} - 2^{x + 4}

2^{x + 4} = 2^{x + 3 + 1}

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

Apply exponent rule:

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

2^{x + 3 + 1} = 2^{1} \cdot 2^{x + 3}

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

Factor out common term

2^{x + 3}

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

Refine

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

Multiply:

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

= - 2^{x + 3}

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Frequently Asked Questions (FAQ)

What is 2^{x+3}-2^{x+4} ?
The solution to 2^{x+3}-2^{x+4} is -2^{x+3}