# Question d577e

Jun 13, 2017

$\frac{1}{\frac{1}{125}}$.

#### Explanation:

${5}^{- 3} = {\left(\frac{1}{5}\right)}^{3} = \frac{1}{125} = 0.008 \text{ }$ (in decimal notation).

Reciprocal $= \frac{1}{\frac{1}{125}} = 125 \to$ Answer

Jun 13, 2017

It's $125$.

#### Explanation:

The reciprocal of $5$ is $\frac{1}{5}$.

$\frac{1}{5}$ to the $- 3$ power $=$ (1/5)^-3=1/(1/5)^3=1/(1/5*1/5*1/5# $= \frac{1}{\frac{1}{125}} = 125$

Jun 13, 2017

The reciprocal is $125$

#### Explanation:

Before we find the reciprocal of the value given, let's simplify it first, because there is a negative index.

${5}^{-} 3 = \frac{1}{5} ^ 3 \text{ } \leftarrow$ law of indices: ${x}^{-} m = \frac{1}{x} ^ m$

The reciprocal of a number is also called its multiplicative inverse.
(Turn it upside down..)

Reciprocal of $2$ is $\frac{1}{2} \text{ and }$Reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$

Reciprocal of $- \frac{1}{4}$ is $- 4 \text{ and }$Reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$

The product of a number and its reciprocal is always $1$

Here we have $\frac{1}{5} ^ 3 = \frac{1}{125}$

The reciprocal is $\frac{125}{1} = 125$