# The blank in the sentence “Using exponential notation, we can write the product 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 5 as ________”.

### 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 1E

(a)

To determine

## To fill: The blank in the sentence “Using exponential notation, we can write the product 5⋅5⋅5⋅5⋅5⋅5 as ________”.

Expert Solution

The complete sentence is “Using exponential notation, we can write the product 555555 as 56_”.

### Explanation of Solution

Definition used:

Exponential notation:

“If a is any real number and n is a positive integer, then the nth power of a is an=aaaan factors where the number a is called as the base and n is called the exponent”.

Calculation:

Consider the given product which is 555555.

Observe that, in the given product the number 5 is multiplied 6 times.

Therefore, by the above definition it can be noted that, here the base is 5 and the exponent is 6.

Therefore, substitute a=5 and n=6 in an and obtain the exponential notation as shown below.

aaaaaa=an555555=56

Thus, the exponential notation of the product 555555 is 56_.

Therefore, the complete sentence is “Using exponential notation, we can write the product 555555 as 56_”.

(b)

To determine

### To fill: The blank in the sentence “In the expression 34 the number 3 is called ____ and the number 4 is called _____”.

Expert Solution

The complete sentence is “In the expression 34 the number 3 is called Base_ and the number 4 is called Exponent_”.

### Explanation of Solution

The given expression is 34.

Use the definition given in part (a) and rewrite 34 as shown below.

34=3333

That is, here the number 3 is repeated 4 times.

Therefore, by the definition of exponential notation it can be noted that the number 3 is the base and the number 4 is the exponent.

Thus, the complete statement is “In the expression 34 the number 3 is called Base_ and the number 4 is called Exponent_”.

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