Lesson 14Expressions with Exponents

Learning Goal

Let’s use the meaning of exponents to decide if equations are true.

Learning Targets

I can decide if expressions with exponents are equal by evaluating the expressions or by understanding what exponents mean.

Warm Up: Which One Doesn’t Belong: Twos

Which one doesn’t belong?

$2 \cdot 2 \cdot 2 \cdot 2$
$2^{4}$
$16$
$4 \cdot 2$

Activity 1: Is the Equation True?

Decide whether each equation is true or false, and explain how you know.

$2^{4} = 2 \cdot 4$
$3 + 3 + 3 + 3 + 3 = 3^{5}$
$5^{3} = 5 \cdot 5 \cdot 5$
$2^{3} = 3^{2}$
$16^{1} = 8^{2}$
$\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = 4 \cdot \frac{1}{2}$
${(\frac{1}{2})}^{4} = \frac{1}{8}$
$8^{2} = 4^{3}$

Activity 2: What’s Your Reason?

In each list, find expressions that are equivalent to each other and explain to your partner why they are equivalent. Your partner listens to your explanation. If you disagree, explain your reasoning until you agree. Switch roles for each list.

(There may be more than two equivalent expressions in each list.)

- $5 \cdot 5$
- $2^{5}$
- $5^{2}$
- $2 \cdot 5$
- $4^{3}$
- $3^{4}$
- $4 \cdot 4 \cdot 4$
- $4 + 4 + 4$
- $6 + 6 + 6$
- $6^{3}$
- $3^{6}$
- $3 \cdot 6$
- $11^{5}$
- $11 \cdot 11 \cdot 11 \cdot 11 \cdot 11$
- $11 \cdot 5$
- $5^{11}$
- $\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}$
- ${(\frac{1}{5})}^{3}$
- $\frac{1}{15}$
- $\frac{1}{125}$
- ${(\frac{5}{3})}^{2}$
- ${(\frac{3}{5})}^{2}$
- $\frac{10}{6}$
- $\frac{25}{9}$

Are you ready for more?

What is the last digit of $3^{1, 000}$ ? Show or explain your reasoning.

Lesson Summary

When working with exponents, the bases don’t have to always be whole numbers. They can also be other kinds of numbers, like fractions, decimals, and even variables. For example, we can use exponents in each of the following ways:

${(\frac{2}{3})}^{4} = \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3}$

${(1.7)}^{3} = (1.7) \cdot (1.7) \cdot (1.7)$

$x^{5} = x \cdot x \cdot x \cdot x \cdot x$

Lesson 14Expressions with Exponents

Learning Goal

Learning Targets

Warm Up: Which One Doesn’t Belong: Twos

Problem 1

Activity 1: Is the Equation True?

Problem 1

Activity 2: What’s Your Reason?

Problem 1

Are you ready for more?

Problem 1

Lesson Summary