Question
Simplify to a single power of 4: \[ \frac{4^{6}}{4^{4}} \] Answer Attempt 1 out of 2 Answer: \( 4 \square \) Submit Answer
Ask by Macdonald Schofield. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \(4^{2}\).
Solution
To simplify \(\frac{4^{6}}{4^{4}}\) to a single power of 4, you can use the properties of exponents. Specifically, when you divide powers with the same base, you subtract the exponents:
\[
\frac{4^{6}}{4^{4}} = 4^{6-4} = 4^{2}
\]
So, the simplified form is:
\[
4^{2}
\]
**Answer:** \(4^{2}\)
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Simplify this solution Bonus Knowledge
When you divide with the same base, you subtract the exponents. So for \( \frac{4^{6}}{4^{4}} \), you perform the operation \( 6 - 4 \), which gives you \( 4^{2} \). Thus, the simplified expression is \( 4^{2} \). So, you would fill in the square with \( 2 \): \( 4 \square \) becomes \( 4^2 \).
