Zero and Negative Exponents
Lesson Plans and Worksheets for Grade 8
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 8
Common Core For Grade 8
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.
Download Worksheet for Common Core Grade 8, Module 1, Lesson 4
Download Worksheet for Common Core Grade 8, Module 1, 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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