Question
(a) Simplify: (1) \( \frac{2^{x+2}+2^{x+3}}{12 \cdot 2^{x}} \)
Ask by Erickson Greene. in South Africa
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is 1.
Solution
Calculate or simplify the expression \( (2^(x+2)+2^(x+3))/(12*2^x) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(2^{x+2}+2^{x+3}\right)}{\left(12\times 2^{x}\right)}\)
- step1: Remove the parentheses:
\(\frac{2^{x+2}+2^{x+3}}{12\times 2^{x}}\)
- step2: Add the terms:
\(\frac{3\times 2^{x+2}}{12\times 2^{x}}\)
- step3: Reduce the fraction:
\(1\)
The simplified form of the expression \( \frac{2^{x+2}+2^{x+3}}{12 \cdot 2^{x}} \) is 1.
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{2^{x+2}+2^{x+3}}{12 \cdot 2^{x}} \), we first factor out \( 2^{x+2} \) from the numerator. So, we have: \[ 2^{x+2} + 2^{x+3} = 2^{x+2}(1 + 2) = 2^{x+2} \cdot 3 \] Now the expression becomes: \[ \frac{2^{x+2} \cdot 3}{12 \cdot 2^{x}} \] Next, we can simplify the fraction: \[ = \frac{3 \cdot 2^{x+2}}{12 \cdot 2^{x}} \] \[ = \frac{3}{12} \cdot \frac{2^{x+2}}{2^{x}} = \frac{1}{4} \cdot 2^{2} = \frac{1}{4} \cdot 4 = 1 \] So the simplified expression is: \[ \boxed{1} \]
