Question
Rewrite the expression (4^-2)^3 using only positive exponents
Answers
Answered by
GPT-4o mini
To rewrite the expression \((4^{-2})^3\) using only positive exponents, we can apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).
1. Start with the original expression:
\[
(4^{-2})^3
\]
2. Apply the power of a power property:
\[
4^{-2 \cdot 3} = 4^{-6}
\]
3. Rewrite the negative exponent using the property \(a^{-n} = \frac{1}{a^n}\):
\[
4^{-6} = \frac{1}{4^6}
\]
Thus, the expression \((4^{-2})^3\) rewritten using only positive exponents is:
\[
\frac{1}{4^6}
\]
1. Start with the original expression:
\[
(4^{-2})^3
\]
2. Apply the power of a power property:
\[
4^{-2 \cdot 3} = 4^{-6}
\]
3. Rewrite the negative exponent using the property \(a^{-n} = \frac{1}{a^n}\):
\[
4^{-6} = \frac{1}{4^6}
\]
Thus, the expression \((4^{-2})^3\) rewritten using only positive exponents is:
\[
\frac{1}{4^6}
\]