$b^{\displaystyle -n} \,=\, \dfrac{1}{b^{\displaystyle \, n}}$

The negative power of a quantity is equal to the reciprocal of the power of the same quantity. It is called negative power rule of the exponents.

$b$ and $n$ are two literals and represent two constants. Assume, they formed two exponential terms $b^{\displaystyle \, n}$ and $b^{\displaystyle -n}$.

The quantity of the positive exponential term $b^{\displaystyle \, n}$ is equal to the reciprocal of the negative exponential term $b^{\displaystyle -n}$.

$b^{\displaystyle -n} \,=\, \dfrac{1}{b^{\displaystyle n}}$

This property is called as negative exponent rule or negative power rule.

Learn how to derive the negative power rule of exponents in algebraic form.

$3^5$ is an exponential term and express its reciprocal in mathematical form.

$\dfrac{1}{3^5}$

According to power zero rule, the number $1$ in the numerator can be written as the $3$ is raised to the power of zero.

$\implies$ $\dfrac{1}{3^5} \,=\, \dfrac{3^0}{3^5}$

In the right-hand side of the equation, the bases are same. Therefore, the quotient of the exponents with same base is the equal to the difference of the exponents with same base as per quotient rule of exponents with same base.

$\implies$ $\dfrac{1}{3^5} \,=\, 3^{\,0-5}$

$\implies$ $\dfrac{1}{3^5} \,=\, 3^{-5}$

$\,\,\, \therefore \,\,\,\,\,\,$ $3^{-5} \,=\, \dfrac{1}{3^5}$

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved