Question

In the following exercises, simplify each expression.

$$\begin{gathered} \left(a\right).6r^{-1} \\ \left(b\right).{\left(6r\right)}^{-1} \\ \left(c\right).{\left(-6r\right)}^{-1} \end{gathered}$$

Short answer

The simplified form of the expressions

$$\begin{gathered} \left(a\right).6r^{-1}=\frac{6}{r} \\ \left(b\right).{\left(6r\right)}^{-1}=\frac{1}{6r} \\ \left(c\right).{\left(-6r\right)}^{-1}=-\frac{1}{6r} \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given information.

The given expression is$6r^{-1}.$

Part (a) Step 2.  Calculate the expression.

Apply the concept of negative exponents.

$a^{-n}=\frac{1}{a^n}$.

So,

$6r^{-1}=\frac{6}{r}$

Part (b) Step 1. Given information.

The given expression is${\left(6r\right)}^{-1}$.

Part (b) Step 2. Calculate the expression.

Apply the concept of negative exponent.

${\left(ab\right)}^{-n}=\frac{1}{{\left(ab\right)}^n}$

So,

${\left(6r\right)}^{-1}=\frac{1}{6r}$.

Part (c) Step 1. Given information.

The given expression is${\left(-6r\right)}^{-1}$.

Part (c) Step 2. Calculate the expression.

Apply the concept of negative exponent.

${\left(-ab\right)}^{-1}=\frac{1}{-ab}$.

So,

${\left(-6r\right)}^{-1}=\frac{1}{-6r}.$