# The blank in the statement “Using exponential notation, we can write 5 3 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 3E

(a)

To determine

## To fill: The blank in the statement “Using exponential notation, we can write 53 as ____”.

Expert Solution

The complete statement is “Using exponential notation, we can write 53 as 513_”.

### Explanation of Solution

Formula used:

Formula for nth root:

an=a1n

Where, a is any real number called as base and n is an integer.

Calculation:

The given expression is 53.

Use the above formula and write the exponential notation as shown below.

53=513

Thus, the complete statement is “Using exponential notation, we can write 53 as 513_”.

(b)

To determine

### To fill: The blank in the statement “Using radicals, we can write 512 as _____”.

Expert Solution

The complete statement is “Using radicals, we can write 512 as 5_”.

### Explanation of Solution

The given expression is 512.

Use the formula mentioned in sub part (a) and write the given exponential expression in the radical form as shown below.

512=52=5

Thus, the complete statement is “Using radicals, we can write 512 as 5_”.

(c)

To determine

Expert Solution

### Explanation of Solution

Formula used:

Formula for nth root:

an=a1n

Where, a is any real number called as base and n is an integer.

Calculation:

Consider the expression, 52.

Using the above formula and simplify the expression as shown below.

52=522=522=5

Thus, the value of 52 is 5.

Now, consider the expression (5)2.

Use the above formula and simplify the expression as follows.

(5)2=(52)2=(512)2=5122=5

Therefore, it can be clearly observed that there is no difference between the values of 52 and (5)2.

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