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What is an exponent?

You know that multiplication represents repeated addition of the same number. For example, the multiplication problem 312 is the same as the addition problem 12+12+12. Writing repeated addition as a multiplication problem shortens both the notation and the solving process.

There is also a shortcut to represent repeated multiplication of the same factor. It is called exponential notation.

Exponential Notation

Exponential notation involves a base and an exponent and is expressed as baseexponent.

The base is the factor that is being multiplied by itself.

The exponent is the number of times you multiply the base by itself.

Write the multiplication problem 444 using exponential notation.

In the multiplication problem 444, the base is 4.

You are multiplying the base, 4, by itself 3 times, so the exponent is 3.

In exponential notation, 444=43.

When a number is expressed using exponential notation, you can simply carry out the multiplication to simplify it.

Simplify 24.

In the exponential notation 24, the number 2 is the base and the number 4 is the exponent.

This notation is the same as 2222.

Multiply the number 2 by itself 4 times in order to simplify 24.

24=2222=16

How well can you work with exponential notation? Use these flashcards to practice. Use your knowledge of exponential notation to answer each question, then click the card to see if you are correct.

Simplify 32.

9

The notation 32=33=9.

Write 54 using repeated multiplication.

5555

The base is 5, and the exponent is 4. This means to multiply the number 5 by itself 4 times.

Write the multiplication problem 131313 using exponential notation.

133

The base is 13, and the exponent is 3 since the number 13 appears 3 times as a factor.

Write the multiplication problem 8888 using exponential notation.

84

The base is 8, and the exponent is 4.

In the exponential notation 19, which number is the base?

1

Exponential notation has the form baseexponent.

Simplify 73.

343

The notation 73 is the same as 777=343.

Write the multiplication problem 1010 using exponential notation.

102

The base is 10, and the exponent is 2.

Write 93 using repeated multiplication.

999

The base is 9, and the exponent is 3.

In the exponential notation 115, which number is the exponent?

5

Exponential notation has the form baseexponent.

Simplify 53.

125

The notation 53 is the same as 555=125.

Cards remaining: 10

Card deck complete!