# Exponents and Exponential Functions

## Objective

Solve mathematical applications of exponential expressions.

## 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

• 7.EE.A.1

## Criteria for Success

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1. Use the properties of exponents in area and volume problems.
2. Simplify expressions using the properties of exponents.
3. Change the base of exponential expressions to write equivalent expressions.

## Tips for Teachers

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This lesson reviews skills and concepts from 8.EE.1. Depending on the needs of your students, this lesson may be skipped or used in a different way. Students may need to spend time developing mastery with Criteria for Success #3, as this will be a useful tool when working with rational exponents in upcoming lessons.

## Anchor Problems

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### Problem 1

The area of a triangle is represented by the expression ${12^4y}$. The base of the triangle is represented by the expression ${3x^2}$. Write an expression that represents the height, $h$.

#### Guiding Questions

• What equation can you write to show the area of the triangle?
• How will you solve the equation for $h$?
• Show that your expression is correct by determining area from the expressions for base and height.

### Problem 2

Find the value of $n$ that makes the equation true.

$8^2\cdot4^n(2^2)^3=16^2\cdot(4^3)^5$

#### Guiding Questions

• How can this problem be solved without calculating the numerical values?
• How are all of the bases related to each other?
• Can you rewrite each exponential so that they all share the same base? What base would that be? Try this simple example: ${9^n=3^{18}}$.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson. They can be used to create a problem set for class (for non-Fishtank Plus users), or as supplementary or additional resources to the pre-made Problem Set (for Fishtank Plus users).

• Include geometric applications similar to Anchor Problem #1 and the Target Task
• Include problems where students rewrite exponential expressions in the same base, similar to Anchor Problem #2
• Include problems from the first few lessons of the unit as needed

A sphere has a radius that is given by the expression ${{1\over2}x^3}$. What expression represents the volume of the sphere in terms of ${\pi}$ and $x$
Determine the value of $n$ in the equation $4\cdot16^n=4^{21}$.