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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

4. Zero and Negative Exponents

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Exercise 8 Page 341

Remember the Product of Powers Property and the Zero Exponent Property.

Product	Product of Powers Property	Power	Value
(- 2)^5 * (- 2)^(- 5)	(- 2)^(5 + (- 5))	(- 2)^0	1

Practice makes perfect

We want to complete the given table.

Product	Product of Powers Property	Power	Value
(- 2)^5 * (- 2)^(- 5)

We will start with the Product of Powers Property.

Product of Powers Property
To multiply powers with the same base, we can add their exponents.

In our case, the exponents are 5 and - 5. Their sum is 5 + ( - 5). Let's fill the second column of our table using the Product of Powers Property!

Product	Product of Powers Property	Power	Value
(- 2)^5 * (- 2)^(- 5)	(- 2)^(5 + ( - 5))

Next, we want to evaluate the sum in the exponent. We know that 5 + (- 5)= 0. Let's put the resulting power in the table!

Product	Product of Powers Property	Power	Value
(- 2)^5 * (- 2)^(- 5)	(- 2)^(5 + (- 5))	(- 2)^0

Finally, we want to evaluate the power. To do this, remember the Zero Exponent Property.

Zero Exponents
For any nonzero number a, a^0=1. The power 0^0 is undefined.

This means that the value of (- 2)^0 is 1. Now, we can fill the table completely!

Product	Product of Powers Property	Power	Value
(- 2)^5 * (- 2)^(- 5)	(- 2)^(5 + (- 5))	(- 2)^0	1

Subchapter links

Try It p.338-339

Self-Assessment for Concepts & Skills p.339

Self-Assessment for Problem Solving p.340

Review & Refresh p.341

Concepts, Skills, & Problem Solving p.341-342