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

Question

?(1 point)
Responses

c
c

c−14
c superscript negative 14 baseline

1c
Start Fraction 1 over c End Fraction

1c49

Answer 1

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

So, we can rewrite the expression:

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

The expression \( c^{-1} \) can also be rewritten as:

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

Therefore, the equivalent expression is:

\[ \frac{1}{c} \]

So the correct response is:

1c (Start Fraction 1 over c End Fraction).