Question

why does (1/14)^-1 = 14?

Answer 1

You know the meaning of a negative exponent, don't you?

\( a^{-n} = \dfrac{1}{a^n} \)

Answer 2

yeah

Answer 3

Now apply that rule to the left side of your question:

\( \left( \dfrac{1}{14} \right)^{-1} \)

\( = \dfrac{1}{ \frac{1}{14} }\)

\(= 1 \div \dfrac{1}{14}\)

\(=\dfrac{1}{1} \cdot \dfrac{14}{1} \)

\(= \dfrac{14}{1} \)

\(= 14 \)