Question
8. \( \frac{4^{3}-4^{2}}{2^{2}}= \)
Ask by Santiago Frank. in China
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value is 12.
Solution
Calculate or simplify the expression \( (4^3-4^2)/2^2 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(4^{3}-4^{2}\right)}{2^{2}}\)
- step1: Remove the parentheses:
\(\frac{4^{3}-4^{2}}{2^{2}}\)
- step2: Subtract the numbers:
\(\frac{48}{2^{2}}\)
- step3: Rewrite the expression:
\(\frac{16\times 3}{2^{2}}\)
- step4: Rewrite the expression:
\(\frac{2^{4}\times 3}{2^{2}}\)
- step5: Reduce the fraction:
\(2^{2}\times 3\)
- step6: Calculate:
\(12\)
The value of \( \frac{4^{3}-4^{2}}{2^{2}} \) is 12.
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Simplify this solution The Deep Dive
To solve \( \frac{4^{3}-4^{2}}{2^{2}} \), we start by calculating the powers: \( 4^3 = 64 \) and \( 4^2 = 16 \). Now, substituting those values in, we get \( 64 - 16 = 48 \). Next, we calculate \( 2^2 = 4 \). Now we can compute the fraction: \( \frac{48}{4} = 12 \). So, \( \frac{4^{3}-4^{2}}{2^{2}} = 12 \).
