 # Zero and Negative Exponents

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Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades

Examples, solutions, and videos to help Grade 8 students learn about zero and negative exponents.

New York State Common Core Math Grade 8, Module 1, Lesson 4 and lesson 5.

Lesson 4 Student Outcomes

Students know that a number raised to the zeroth power is equal to one.

Students recognize the need for the definition to preserve the properties of exponents.

Lesson 4 Opening Exercise

For any numbers x, y and any positive integers m, n, the following holds:

xm • xn = xm+n
(xm)n = xmn
(xy)n = xnyn

Definition: For any positive number x, we define x0 = 1.

Examples

1. Simplify the following expression as much as possible.
915 • 9-10 • 9-5 =

410/410 • 70 =

Lesson 5 Student Outcomes

Students know the definition of a number raised to a negative exponent.

Students simplify and write equivalent expressions that contain negative exponents.

Lesson 5 Opening Exercise

For any numbers x, y and any positive integers m, n, the following holds:

xm • xn = xm+n
(xm)n = xmn
(xy)n = xnyn

Definition: For any positive number x and for any positive integer n, we define x-n = 1/xn.
Note that this definition of negative exponents says x-1 is just the reciprocal 1/x of x.

xm ÷ xn = xm-n
(x/y)n = xn/yn

Examples

2-1 =
3-2 =
(4/5)-3 =
5-2 =
1/89 =
3 • 2-4 =

Let x and y be non-zero numbers
x-3 =
1/x9 =
xy -4 =

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