# The value of expression 200 − 32 without negative exponents. ### 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, Problem 4T

(a)

To determine

## The value of expression 200−32 without negative exponents.

Expert Solution

The value of expression 20032 is 62 .

### Explanation of Solution

Given:

The expression is 20032 .

Calculation:

Solve the given expression of square roots,

20032=1002162=1002162=10242=62

Thus, the value of expression 20032 is 62 .

(b)

To determine

### The simplest form of expression (3a3b3)(4ab2)2 .

Expert Solution

The simplest form of expression (3a3b3)(4ab2)2 is 48a5b7 .

### Explanation of Solution

Given:

The expression is (3a3b3)(4ab2)2 .

Calculation:

Use the laws of exponents to solve the given expression,

(3a3b3)(4ab2)2=(3a3b3)(16a2b4)=48a3+2b3+4=48a5b7

Thus, the simplest form of expression (3a3b3)(4ab2)2 is 48a5b7 .

(c)

To determine

### The simplest form of expression (3x3/2y3x2y−1/2)−2 .

Expert Solution

The simplest form of expression (3x3/2y3x2y1/2)2 is x9y7 .

### Explanation of Solution

Given:

The expression is (3x3/2y3x2y1/2)2 .

Calculation:

Use the laws of exponents with rational exponents to solve the given expression,

(3x3/2y3x2y1/2)2=1(3x3/2y3x2y1/2)2=(x2y1/23x3/2y3)2=(x2y1/2)2(3x3/2y3)2=x2+2y1/2+29x3/2+2y3+2

Further, solve the above expression to get simplest form,

(3x3/2y3x2y1/2)2=x22y1/229x3/22y32=x4y19x3y6=x439y5+1=x9y7

Thus, the simplest form of expression (3x3/2y3x2y1/2)2 is x9y7 .

(d)

To determine

### The simplest form of expression x2+3x+2x2−x−2 .

Expert Solution

The simplest form of expression x2+3x+2x2x2 is x+2x2 .

### Explanation of Solution

Given:

The function is x2+3x+2x2x2 .

Calculation:

Factor the given function to get simplest form,

x2+3x+2x2x2=x2+2x+x+2x22x+x2=x(x+2)+1(x+2)x(x2)+1(x+2)=(x+1)(x+2)(x+1)(x2)=x+2x2

Thus, the simplest form of expression x2+3x+2x2x2 is x+2x2 .

(e)

To determine

### The simplest form of expression x2x2−4−x+1x+2 .

Expert Solution

The simplest form of expression x2x24x+1x+2 is 1x2 .

### Explanation of Solution

Given:

The function is x2x24x+1x+2 .

Calculation:

First, solve than factor the given function to get simplest form,

x2x24x+1x+2=x2(x+2)(x+1)(x2(2)2)(x2(2)2)(x+2)=x2(x+2)(x+1)(x+2)(x2)(x+2)(x2)(x+2)=(x+2)(x2(x+1)(x2))(x+2)(x2)(x+2)=x2x2+x+2(x2)(x+2)

Further, solve above expression to get simplest form,

x2x24x+1x+2=x2x2+x+2(x2)(x+2)=x+2(x2)(x+2)=1x2

Thus, the simplest form of expression x2x24x+1x+2 is 1x2 .

(f)

To determine

### The simplest form of expression yx−xy1y−1x .

Expert Solution

The simplest form of expression yxxy1y1x is (x+y) .

### Explanation of Solution

Given:

The function is yxxy1y1x .

Calculation:

First, solve than factor the given function to get simplest form,

yxxy1y1x=y2x2xyxyxy=y2x2xyxyxy=y2x2xy=(y+x)(yx)xy

Further, solve above expression to get simplest form,

yxxy1y1x=(y+x)(yx)xy=(xy)(x+y)xy=(x+y)

Thus, the simplest form of expression yxxy1y1x is (x+y) .

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