Question
Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. \( 4^{-2} \) 1
Ask by Bowers Campos. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{1}{16} \)
Solution
To simplify \( 4^{-2} \) and express the answer with positive exponents, follow these steps:
1. **Understand Negative Exponents:**
A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent.
\[
a^{-n} = \frac{1}{a^n}
\]
2. **Apply the Rule to \( 4^{-2} \):**
\[
4^{-2} = \frac{1}{4^2}
\]
3. **Calculate \( 4^2 \):**
\[
4^2 = 16
\]
4. **Final Simplified Form:**
\[
4^{-2} = \frac{1}{16}
\]
**Answer:**
\[
\frac{1}{16}
\]
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Simplify this solution Bonus Knowledge
The expression \( 4^{-2} \) can be simplified by using the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Therefore, \( 4^{-2} \) becomes \( \frac{1}{4^2} \). Calculating \( 4^2 \) gives us \( 16 \), so we have \( \frac{1}{16} \). This is the positive exponent form of the original expression. If you're ever unsure about negative exponents, remember they simply indicate that you're dealing with the reciprocal of the base raised to the corresponding positive exponent. In this case, flipping \( 4^{-2} \) into a positive exponent is a breeze!
