Chapter 5: Q. 118 (page 521)

In the following exercises, simplify each expression using the Power Property.
$(a) {(x^{2})}^{y} (b) {(7^{a})}^{b} (c) {(a^{9})}^{- 10}$

Short Answer

Expert verified

The simplified expression are:

$(a) {(x^{2})}^{y} = x^{2 y} (b) {(7^{a})}^{b} = 7^{a b} (c) {(a^{9})}^{- 10} = a^{- 90}$

Step by step solution

Step 1. Power properties for exponents

If $a$ is a real number and $m$ and $n$ are integers, then

${(a^{m})}^{n} = a^{m \cdot n}$

Part a Step 1. Given information

The given expression is ${(x^{2})}^{y}$ .

We have to simplify the given expression using Power property for exponent.

Part a Step 2. Simplify

Using Power property for exponent,

$\begin{matrix} {(x^{2})}^{y} = x^{2 \cdot y} \\ = x^{2 y} \end{matrix}$

So, the simplified expression is ${(x^{2})}^{y} = x^{2 y}$

Part b Step 1. Given information

The given expression is ${(7^{a})}^{b}$ .

We have to simplify the given expression using Power property for exponent.

Part b Step 2. Simplify

Using the Power property for exponents,

$\begin{matrix} {(7^{a})}^{b} = 7^{a \cdot b} \\ = 7^{a b} \end{matrix}$

So, the simplified expression is ${(7^{a})}^{b} = 7^{a b}$

Part c Step 1. Given information

The given expression is ${(a^{9})}^{- 10}$ .

We have to simplify the given expression using Power property for exponent.

Part c Step 2. Simplify

Using Power properties for exponent,

$\begin{matrix} {(a^{9})}^{- 10} = a^{9 \cdot (- 10)} \\ = a^{- 90} \end{matrix}$

So, the simplified expression is ${(a^{9})}^{- 10} = a^{- 90}$

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In the following exercises, simplify each expression using the Power Property.
$(a) {(x^{2})}^{y} (b) {(7^{a})}^{b} (c) {(a^{9})}^{- 10}$

Short Answer

Step by step solution

Step 1. Power properties for exponents

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2. Simplify

Part c Step 1. Given information

Part c Step 2. Simplify

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In the following exercises, simplify each expression using the Power Property.ax2yb7abca9-10

Short Answer

Step by step solution

Step 1. Power properties for exponents

Part a Step 1. Given information

Part a Step 2. Simplify

Part b Step 1. Given information

Part b Step 2. Simplify

Part c Step 1. Given information

Part c Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Power Property.
$(a) {(x^{2})}^{y} (b) {(7^{a})}^{b} (c) {(a^{9})}^{- 10}$