(3^-4)^4

1 answer

To simplify the expression \((3^{-4})^4\), we need to use the power of a power property, which states that \((a^b)^c = a^{bc}\).

So, applying this property to our expression, we have:
\((3^{-4})^4 = 3^{-4\times 4} = 3^{-16}\).

To further simplify, we can use the definition of negative exponents, which states that \(a^{-n} = \frac{1}{a^n}\). Applying this definition to our expression:

\(3^{-16} = \frac{1}{3^{16}}\).

Therefore, \((3^{-4})^4\) simplifies to \(\frac{1}{3^{16}}\).