Question
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Answer
The simplified form is 8.
Solution
Calculate or simplify the expression \( 2^(x+5)/2^(x+2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{2^{x+5}}{2^{x+2}}\)
- step1: Multiply by \(a^{-n}:\)
\(2^{x+5}\times 2^{-\left(x+2\right)}\)
- step2: Calculate:
\(2^{x+5}\times 2^{-x-2}\)
- step3: Multiply:
\(2^{x+5-x-2}\)
- step4: Calculate:
\(2^{3}\)
- step5: Evaluate the power:
\(8\)
The simplified form of \( \frac{2^{x+5}}{2^{x+2}} \) is \( 8 \).
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Simplify this solution Extra Insights
To simplify the expression \( \frac{2^{x+5}}{2^{x+2}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). By applying this, we subtract the exponents: \( (x + 5) - (x + 2) = 3 \). So, the expression simplifies to \( 2^3 \), which equals 8. In exponential terms, this simplification becomes an easy way to handle fractions with the same base—just subtract the exponents. It’s like decluttering your math!
