Question

Which expression is equivalent to (c^−7)1/7

Answer 1

To simplify the expression \((c^{-7})^{1/7}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this property:

\[
(c^{-7})^{1/7} = c^{-7 \cdot \frac{1}{7}} = c^{-1}
\]

Now, \(c^{-1}\) can be expressed as:

\[
c^{-1} = \frac{1}{c}
\]

So, the expression \((c^{-7})^{1/7}\) is equivalent to \(\frac{1}{c}\).