Chapter 5: Q 117. (page 521)

In the following exercises, simplify each expression using the Power Property
$(a) {(y^{3})}^{x} (b) {(5^{x})}^{y} (c) {(q^{6})}^{- 8}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(y^{3})}^{x} = y^{3 x} (b) {(5^{x})}^{y} = 5^{x y} (c) {(q^{6})}^{- 8} = q^{- 48}$

Step by step solution

Step 1. Power property 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 ${(y^{3})}^{x}$ .

We have to simplify the expression using Power property for exponents.

Part a Step 2. Simplify

Using the Power property for exponent,

$\begin{matrix} {(y^{3})}^{x} = y^{3 \cdot x} \\ = y^{3 x} \end{matrix}$

So, the simplified expression is ${(y^{3})}^{x} = y^{3 x}$

Part b Step 1. Given information

The given expression is ${(5^{x})}^{y}$ .

We have to simplify the expression using Power property for exponents.

Part b Step 2. Simplify

Using the Product power for exponent,

$\begin{matrix} {(5^{x})}^{y} = 5^{x \cdot y} \\ = 5^{x y} \end{matrix}$

So, the simplified expression is ${(5^{x})}^{y} = 5^{x y}$

Part c Step 1. Given information

The given expression is ${(q^{6})}^{- 8}$ .

We have to simplify the expression using Power property for exponents.

Part c Step 2. Simplify

Using the Power property for exponent,

$\begin{matrix} {(q^{6})}^{- 8} = q^{6 \cdot (- 8)} \\ = q^{- 48} \end{matrix}$

So, the simplified expression is ${(q^{6})}^{- 8} = q^{- 48}$

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In the following exercises, simplify each expression using the Power Property
$(a) {(y^{3})}^{x} (b) {(5^{x})}^{y} (c) {(q^{6})}^{- 8}$

Short Answer

Step by step solution

Step 1. Power property 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 Propertyay3xb5xycq6-8

Short Answer

Step by step solution

Step 1. Power property 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

Geometry

Decision Maths

Statistics

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify each expression using the Power Property
$(a) {(y^{3})}^{x} (b) {(5^{x})}^{y} (c) {(q^{6})}^{- 8}$