# Exponential Notation

Videos and solutions to help Grade 8 students learn about exponential notation.

New York State Common Core Math Grade 8, Module 1, Lesson 1.

Related Topics:
Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

Student Outcomes

Students know what it means for a number to be raised to a power and how to represent the repeated multiplication symbolically.

Students know the reason for some bases requiring parentheses.

Opening Exercise

Without solving, what is another way to rewrite:
3 + 3 + 3 + 3 + 3 =

How would we rewrite:
3 × 3 × 3 × 3 × 3 =

56 means 5 × 5 × 5 × 5 × 5 × 5

You have seen this kind of notation before, it is called exponential notation. In general, for any number x and any positive integer n,

xn = (x • x • • • x) n times

The number xn is called x raised to the n-th power, n is the exponent of in xn and x is the base of xn.

Examples

5 × 5 × 5 × 5 × 5 × 5 =

9/7 × 9/7 × 9/7 × 9/ 7 =

(-4/11)3 =

(-2)6 =

(3.8)4 =

The number xn is called x raised to the n-th power, n is the exponent of x in xn and x is the base of xn.

x2 is called the square of x, and x3 is its cube.

You have seen this kind of notation before when you gave the expanded form of a whole number for powers of 10, it is called exponential notation.

Exercises
Exercises 1 - 10
Exercise 11
Will these products be positive or negative? How do you know?
Exercise 12
Is it necessary to do all of the calculations to determine the sign of the product? Why or why not?
Exercise 13
Fill in the blanks about whether the number is positive or negative.
If n is a positive even number, then (-55)n is _____.
If n is a positive odd number, then (-72.4)n is _____.
Exercise 14
Is Josie correct? How do you know?

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