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.

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Common Core For Grade 8

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:

x^{m} • x^{n} = x^{m+n}

(x^{m})^{n }= x^{mn}

(xy)^{n} = x^{n}y^{n}

Definition: For any positive number x, we define x^{0} = 1.

Examples

1. Simplify the following expression as much as possible.

9^{15 }• 9^{-10} • 9^{-5} =

4^{10}/4^{10} • 7^{0} =

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:

x^{m} • x^{n} = x^{m+n}

(x^{m})^{n }= x^{mn}

(xy)^{n} = x^{n}y^{n}

Definition: For any positive number x and for any positive integer n, we define x^{-n} = 1/x^{n}.

Note that this definition of negative exponents says x^{-1} is just the reciprocal 1/x of x.

x^{m} ÷ x^{n} = x^{m-n}

(x/y)^{n} = x^{n}/y^{n}

Examples

2^{-1} =

3^{-2} =

(4/5)^{-3} =

5^{-2} =

1/8^{9} =

3 • 2^{-4 }=

Let x and y be non-zero numbers

x^{-3} =

1/x^{9} =

xy
^{-4}
=

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