BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 34E

  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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