# the given expression.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.2, Problem 33E
To determine

## To simplify: the given expression.

Expert Solution

(x2+4)x .

### Explanation of Solution

Given information:

Given expression

16x+x5

Calculation:

Consider the given expression.

16x+x5

The expression can be simplified as shown:

Here, we have n th roots, in this case, because they are square roots, n=2 .

16x2+x52

Let’s start by using the first property of n th roots, which states

Rewrite the first term using this.

162x2+x52

This simplifies to

Now, we can use the definition of the n th roots, which is

a1n=an

And rewrite the second term. The first term can just be left as a square root for now.

x4+(x5)12

The third law of exponents, which states

(am)n=amn

Allows us to multiply the exponents of the second term.

x4+x52

The first law of exponents, which states

aman=am+n ,

Helps us split up the second term (2+12=52) .

x4+x2x12x4+x2x

Factor the square root.

(x2+4)x

The simplified expression is (x2+4)x .

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