Lesson 7: Using Negative Exponents

Using Negative Exponents

5 min

Narrative

This Warm-up prepares students to work with expressions involving negative exponents. Students have studied exponents and their properties in grade 8 and encountered negative exponents at that time. The goal here is to review the fact that for integer exponents $m$ and $n$ and a non-zero base $b$ , this property holds: $b^m \boldcdot b^n = b^{m+n}$ .

Student Task

How would you rewrite each of the following as an equivalent expression with a single exponent?

$2^4 \boldcdot 2^0$
$2^4 \boldcdot 2^{\text-1}$
$2^4 \boldcdot 2^{\text-3}$
$2^4 \boldcdot 2^{\text-4}$

Sample Response

$2^4$
$2^3$
$2^1$
$2^0$

Activity Synthesis (Teacher Notes)

Review, if needed, the conventions that $2^0 = 1$ and $2^{-1} = \frac{1}{2}$ , emphasizing that these conventions guarantee that $2^a \boldcdot 2^b = 2^{a+b}$ for any two integers $a$ and $b$ .

Standards

Building On

8.EE.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.
8.EE.A.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, $3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27$.

15 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Using Negative Exponents

5 min

Narrative

Student Task

How would you rewrite each of the following as an equivalent expression with a single exponent?

$2^4 \boldcdot 2^0$
$2^4 \boldcdot 2^{\text-1}$
$2^4 \boldcdot 2^{\text-3}$
$2^4 \boldcdot 2^{\text-4}$

Sample Response

$2^4$
$2^3$
$2^1$
$2^0$

Activity Synthesis (Teacher Notes)

Review, if needed, the conventions that $2^0 = 1$ and $2^{-1} = \frac{1}{2}$ , emphasizing that these conventions guarantee that $2^a \boldcdot 2^b = 2^{a+b}$ for any two integers $a$ and $b$ .

Standards

Building On

8.EE.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.
8.EE.A.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, $3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27$.

Using Negative Exponents

Warm-upExponent Rules5 minKCs

Narrative

Student Task

Sample Response

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Knowledge Components

Using Negative Exponents

Warm-upExponent Rules5 minKCs

Narrative

Student Task

Sample Response

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5 min

15 min

15 min

5 min

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15 min