# 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 34E
To determine

## To simplify: the given expression.

Expert Solution

y3(23y1) .

### Explanation of Solution

Given information:

Given expression

2y43y3

Calculation:

Consider the given expression.

2y43y3

The expression can be simplified as shown:

Here, we have n th roots, in this case, because they are square roots, n=3 .

abn=anbn

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

Rewrite the first term using this.

23y43y3

If we use y4=yy3 , we can simplify more,

23yy33y3

Using the first property of n th roots, which states

abn=anbn

We can rewrite the first term,

23y3y33y3

Now, we can use the fourth property of n th roots, which states

ann=aifnisodd

To write y33 as simply y . This gives us

23y3yy3

We can factor y3 out.

y3(23y1)

The final simplified expression.

y3(23y1)

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