Question

Which of the following pair expresses reciprocal law of exponents?

• A. $a^m=\frac{1}{a^m}$ and $a^{-m}=\frac{1}{a^{-m}}$
• B. $a^m=\frac{1}{a^{-m}}$ and $a^{-m}=\frac{-1}{a^m}$
• C. $a^m=\frac{1}{a^{-m}}$ and $a^{-m}=\frac{1}{a^m}$
• D. $a^m=\frac{-1}{a^m}$ and $a^{-m}=\frac{1}{a^m}$

Answer 1

The correct option is C $a^m=\frac{1}{a^{-m}}$ and $a^{-m}=\frac{1}{a^m}$

The reciprocal law of exponents states that any non - zero number raised to a power equals its reciprocal raised to the negative power and vice-versa.
$\therefore a^m=\frac{1}{a^{-m}}$ and $a^{-m}=\frac{1}{a^m}$, where $a\ne 0$