Chapter 7.1, Problem 3P

(a)

To determine

To find: The value of the expression $n^{-4}{w}^0$ when $n=-2$ and $w=5$ .

Answer to Problem 3P

The value of the expression $n^{-4}{w}^0$ is $\frac{1}{16}$ .

Explanation of Solution

Given information:

The given expression is $n^{-4}{w}^0$ . The values are $n=-2$ and $w=5$ .

Calculation:

Solve the expression by substituting the values.

  $\begin{array}{c}{n}^{-4}{w}^0={\left(-2\right)}^{-4}\cdot {\left(5\right)}^0\\ =\frac{1}{{\left(-2\right)}^4}\cdot 1\left\{5^0=1\right\}\\ =\frac{1}{16}\end{array}$

Conclusion:

Therefore, the value of the expression $n^{-4}{w}^0$ is $\frac{1}{16}$ .

(b)

To determine

To find: The value of the expression $\frac{n^{-1}}{w^2}$ when $n=-2$ and $w=5$ .

Answer to Problem 3P

The value of the expression $\frac{n^{-1}}{w^2}$ is $-\frac{1}{50}$ .

Explanation of Solution

Given information:

The given expression is $\frac{n^{-1}}{w^2}$ . The values are $n=-2$ and $w=5$ .

Calculation:

Solve the expression by substituting the values.

  $\begin{array}{c}\frac{n^{-1}}{w^2}=\frac{{\left(-2\right)}^{-1}}{5^2}\\ =\frac{1}{\left(-2\right)\cdot 25}\\ =-\frac{1}{50}\end{array}$

Conclusion:

Therefore, the value of the expression $\frac{n^{-1}}{w^2}$ is $-\frac{1}{50}$ .

(c)

To determine

To find: The value of the expression $\frac{n^0}{w^6}$ when $n=-2$ and $w=5$ .

Answer to Problem 3P

The value of the expression $\frac{n^0}{w^6}$ is $\frac{1}{15625}$ .

Explanation of Solution

Given information:

The given expression is $\frac{n^0}{w^6}$ . The values are $n=-2$ and $w=5$ .

Calculation:

Solve the expression by substituting the values.

  $\begin{array}{c}\frac{n^0}{w^6}=\frac{{\left(-2\right)}^0}{5^6}\\ =\frac{1}{15625}\left\{{\left(-2\right)}^0=1\right\}\end{array}$

Conclusion:

Therefore, the value of the expression $\frac{n^0}{w^6}$ is $\frac{1}{15625}$ .

(d)

To determine

To find: The value of the expression $\frac{1}{n{w}^{-1}}$ when $n=-2$ and $w=5$ .

Answer to Problem 3P

The value of the expression $\frac{1}{n{w}^{-1}}$ is $-\frac{5}{2}$ .

Explanation of Solution

Given information:

The given expression is $\frac{1}{n{w}^{-1}}$ . The values are $n=-2$ and $w=5$ .

Calculation:

Solve the expression by substituting the values.

  $\begin{array}{c}\frac{1}{n{w}^{-1}}=\frac{1}{\left(-2\right)\cdot 5^{-1}}\\ =-\frac{5}{2}\end{array}$

Conclusion:

Therefore, the value of the expression $\frac{1}{n{w}^{-1}}$ is $-\frac{5}{2}$ .

(e)

To determine

To check: Whether the expression $n^0{w}^0$ is easier to evaluate by simplification first or substitution first.

Answer to Problem 3P

The expression $n^0{w}^0$ is easier to evaluate by simplification first.

Explanation of Solution

Given information:

The given expression is $n^0{w}^0$ . The values are $n=-2$ and $w=3$ .

Calculation:

Since the value of any number or variable with zero power is always 1. So, the value of the expression will be 1. If the values of $n$ and $w$ are substituted, the result will be same. Therefore, the simplification method will be preferred.

Conclusion:

Therefore, the expression $n^0{w}^0$ is easier to evaluate by simplification first.