Chapter 7.1, Problem 55PPE

a.

To determine

To Complete: The patterns using powers of 5.

  $\begin{array}{l}\frac{1}{5^2}=\_\_\_\\ \frac{1}{5^1}=\_\_\_\\ \frac{1}{5^0}=\_\_\_\\ \frac{1}{5^{-1}}=\_\_\_\\ \frac{1}{5^{-2}}=\_\_\_\end{array}$

Answer to Problem 55PPE

The required answer is: $\begin{array}{l}\frac{1}{5^2}=5^{-2}\\ \frac{1}{5^1}=5^{-1}\\ \frac{1}{5^0}=5^0\\ \frac{1}{5^{-1}}=5^1\\ \frac{1}{5^{-2}}=5^2\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}\frac{1}{5^2}=\_\_\_\\ \frac{1}{5^1}=\_\_\_\\ \frac{1}{5^0}=\_\_\_\\ \frac{1}{5^{-1}}=\_\_\_\\ \frac{1}{5^{-2}}=\_\_\_\end{array}$

Calculation:

  $\begin{array}{l}\frac{1}{5^2}=5^{-2}\\ \frac{1}{5^1}=5^{-1}\\ \frac{1}{5^0}=5^0\\ \frac{1}{5^{-1}}=5^1\\ \frac{1}{5^{-2}}=5^2\end{array}$

(Using the definition of negative exponent and zero exponent)

b.

To determine

To write: $\frac{1}{5^{-4}}$ using a positive exponent.

Answer to Problem 55PPE

The required answer is $5^4$ .

Explanation of Solution

Given information:

The expression $\frac{1}{5^{-4}}$

Calculation:

  $\begin{array}{l}\frac{1}{5^{-4}}\\ =5^4\end{array}$

(Using the definition of negative exponent)

c.

To determine

To rewrite: $\frac{1}{a^{-n}}$ as a power of a.

Answer to Problem 55PPE

The required answer is $a^n$ .

Explanation of Solution

Given information:

The expression $\frac{1}{a^{-n}}$

Calculation:

  $\begin{array}{l}\frac{1}{a^{-n}}\\ =a^n\end{array}$

(Using the definition of negative exponent)