Question
left parenthesis, 3, to the power 4 , right parenthesis, to the power minus 4 , question mark(3
4
)
−4
4
)
−4
Answers
GPT-4o mini
To simplify the expression \((3^4)^{-4}\), you can follow these steps:
1. Start with the expression:
\[
(3^4)^{-4}
\]
2. Apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(3^4)^{-4} = 3^{4 \cdot (-4)} = 3^{-16}
\]
3. To express \(3^{-16}\) in a more conventional form, use the property \(a^{-n} = \frac{1}{a^n}\):
\[
3^{-16} = \frac{1}{3^{16}}
\]
So, the simplified form of \((3^4)^{-4}\) is:
\[
\frac{1}{3^{16}}
\]
1. Start with the expression:
\[
(3^4)^{-4}
\]
2. Apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(3^4)^{-4} = 3^{4 \cdot (-4)} = 3^{-16}
\]
3. To express \(3^{-16}\) in a more conventional form, use the property \(a^{-n} = \frac{1}{a^n}\):
\[
3^{-16} = \frac{1}{3^{16}}
\]
So, the simplified form of \((3^4)^{-4}\) is:
\[
\frac{1}{3^{16}}
\]