# The expression 200 − 32 . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

## To simplify: The expression 200−32.

Expert Solution

The expression 20032 is simplified as 62.

### Explanation of Solution

Consider the expression 20032.

Observe that,

200=2×2×2×5×5=(2)2×(5)2×2=(2×5)2=102

Again observe that,

32=2×2×2×2×2=(2)2×(2)2×2=(2×2)2=42

Substitute 200=102 and 32=42 in 20032 and simplify the above expression as follows,

20032=10242=(104)2=62

Thus, the expression 20032 is simplified as 62.

(b)

To determine

### To simplify: The expression (3a3b3)(4ab2)2.

Expert Solution

The expression (3a3b3)(4ab2)2 is simplified as 48a5b7.

### Explanation of Solution

Consider the expression (3a3b3)(4ab2)2.

Simplify the above expression as follows,

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

Thus, the expression (3a3b3)(4ab2)2 is simplified as 48a5b7.

(c)

To determine

### To simplify: The expression (3x32y3x2y−12)−2.

Expert Solution

The expression (3x32y3x2y12)2 is simplified as x9y7.

### Explanation of Solution

Consider the expression (3x32y3x2y12)2.

Simplify the above expression as follows,

(3x32y3x2y12)2=(x2y123x32y3)2(a1=1a)=(x2y12)2(3x32y3)2=(x4y19x3y6)=(x49x3y7)

=x9y7

Thus, the expression (3x32y3x2y12)2 is simplified as x9y7.

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