Chapter 5: Q.98 (page 520)

Use the Definition of a Negative Exponent
In the following exercises, simplify each expression.
$(a) b^{- 4} (b) 10^{- 2} (c) \frac{1}{c^{- 5}} (d) \frac{1}{5^{- 2}}$

Short Answer

Expert verified

The simplified form of the expressions are:

$\begin{array}{rcl} (a) b^{- 4} & = & \frac{1}{b^{4}} \\ (b) 10^{- 2} & = & \frac{1}{10^{2}} \\ (c) \frac{1}{c^{- 5}} & = & c^{5} \\ (d) \frac{1}{5^{- 2}} & = & 5^{2} \end{array}$

Step by step solution

Step 1

The properties of negative exponents:

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

Step 2

Use the negative property $a^{- n} = \frac{1}{a^{n}}$ to simplify the expressions:

$\begin{array}{rcl} (a) b^{- 4} & = & \frac{1}{b^{4}} \\ (b) 10^{- 2} & = & \frac{1}{10^{2}} \end{array}$

Step 3

Use the negative property $\frac{1}{a^{- n}} = a^{n}$ to simplify the expressions:

$\begin{array}{rcl} (c) \frac{1}{c^{- 5}} & = & c^{5} \\ (d) \frac{1}{5^{- 2}} & = & 5^{2} \end{array}$

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Use the Definition of a Negative Exponent
In the following exercises, simplify each expression.
$(a) b^{- 4} (b) 10^{- 2} (c) \frac{1}{c^{- 5}} (d) \frac{1}{5^{- 2}}$

Short Answer

Step by step solution

Step 1

Step 2

Step 3

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Use the Definition of a Negative ExponentIn the following exercises, simplify each expression.ab-4b10-2c1c-5d15-2

Short Answer

Step by step solution

Step 1

Step 2

Step 3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Statistics

Logic and Functions

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use the Definition of a Negative Exponent
In the following exercises, simplify each expression.
$(a) b^{- 4} (b) 10^{- 2} (c) \frac{1}{c^{- 5}} (d) \frac{1}{5^{- 2}}$