Chapter 7.1, Problem 2P

a.

To determine

To Simplify: The expression $x^{-9}$ .

Answer to Problem 2P

The required answer is: $\frac{1}{x^9}$

Explanation of Solution

Given information:

The expression $x^{-9}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $x^{-9}$

(Applying negative exponent concept)

  $=\frac{1}{x^9}$

b.

To determine

To Simplify: The expression $\frac{1}{n^{-3}}$ .

Answer to Problem 2P

The required answer is: $n^3$

Explanation of Solution

Given information:

The expression $\frac{1}{n^{-3}}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $\begin{array}{l}\frac{1}{n^{-3}}\\ =1÷n^{-3}\end{array}$

(Applying negative exponent concept)

  $=1÷\frac{1}{n^3}$

Multiplying the reciprocal of $\frac{1}{n^3}$

  $\begin{array}{l}=1\cdot n^3\\ =n^3\end{array}$

c.

To determine

To Simplify: The expression $4c^{-3}b$ .

Answer to Problem 2P

The required answer is: $\frac{4b}{c^3}$

Explanation of Solution

Given information:

The expression $4c^{-3}b$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $4c^{-3}b$

(Applying negative exponent concept)

  $=\frac{4b}{c^3}$

d.

To determine

To Simplify: The expression $\frac{2}{a^{-3}}$ .

Answer to Problem 2P

The required answer is: $2a^3$

Explanation of Solution

Given information:

The expression $\frac{2}{a^{-3}}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $\begin{array}{l}\frac{2}{a^{-3}}\\ =2÷a^{-3}\end{array}$

(Applying negative exponent concept)

  $=2÷\frac{1}{a^3}$

Multiplying the reciprocal of $\frac{1}{a^3}$

  $\begin{array}{l}=2\cdot a^3\\ =2a^3\end{array}$

e.

To determine

To Simplify: The expression $\frac{n^{-5}}{m^2}$ .

Answer to Problem 2P

The required answer is: $\frac{1}{n^5{m}^2}$

Explanation of Solution

Given information:

The expression $\frac{n^{-5}}{m^2}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $\frac{n^{-5}}{m^2}$

(Applying negative exponent concept)

  $\begin{array}{l}=\frac{\frac{1}{n^5}}{m^2}\\ =\frac{1}{n^5{m}^2}\end{array}$