# Exponents and Exponential Functions

## Objective

Use exponent rules to analyze and rewrite expressions with non-negative exponents.

## Common Core Standards

### Core Standards

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• 8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.

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• 6.EE.A.1

## Criteria for Success

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1. Use the power, product, and quotient rules to simplify exponential expressions with non-negative exponents.
2. Use the order of operations and properties of exponents to write equivalent expressions and to justify why two expressions are not equivalent.

## Tips for Teachers

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This lesson reviews skills and concepts from 8.EE.1 in order to set students up for success with the rest of the unit. Depending on the needs of your students, this lesson may be skipped or used in a different way.

## Anchor Problems

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### Problem 1

Which expressions are equivalent to ${{(x^5x^4)^3}\over{x^2}}$? Select all that apply.

a.   ${x^{25}}$

b.   ${x^{30}}$

c.   ${{x^{12}}\over{x^2}}$

d.   ${{x^{27}}\over{x^2}}$

e.   ${{x^{60}}\over{x^2}}$

f.   ${{(x^9)^3}\over x^2}$

g.   ${{(x^{20})^3}\over x^2}$

### Problem 2

Simplify the following expression using the properties of exponents.

${{{8a^4(7b)^3}\over 7ab^2} \times \left({7^2a}\over{8b^2}\right)^5}$

### Problem 3

Is ${(x-y)^2}$ equivalent to ${(x^2-y^2)}$? Justify your answer.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

${{3x^3(y^2)^3}\over(2x^2)^3y^4}$