Q. 107 - Intermediate Algebra

Question

Use the definition of Negative Exponent to simplify (a) $3·5^{-1}$ (b) ${\left(3·5\right)}^{-1}.$

Step-by-Step Solution

Answer

The simplified equation is (a) $\frac{3}{5}$ (b) $\frac{1}{15}.$

Part (a). Step 1. Given information.

The given expression is $3·5^{-1}$.

We have to simplify the expression.

Part (a). Step 2. Definition of Negative exponents.

If $n$ is an integer and $a\ne 0$, then

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

Part (a). Step 3. Simplify the expression.

Using the definition of Negative exponents

$$\begin{gathered} 3·5^{-1}=3·\frac{1}{5} \\ =\frac{3}{5} \end{gathered}$$

So, $3·5^{-1}=\frac{3}{5}.$

Part (b). Step 1. Given information.

The given expression is ${\left(3·5\right)}^{-1}$.

We have to simplify the expression.

Part (b). Step 2. Definition of Negative Exponents.

If $n$ is an integer and $a\ne 0$ then

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

Part (b). Step 3. Simplify the expression.

Using the definition of Negative Exponents

$$\begin{gathered} {\left(3·5\right)}^{-1}=\left(\frac{1}{3}·\frac{1}{5}\right) \\ =\frac{1}{15} \end{gathered}$$.

So, ${\left(3·5\right)}^{-1}=\frac{1}{15}.$