# Lesson 6

What about Other Bases?

Let’s explore exponent patterns with bases other than 10.

### Problem 1

Priya says “I can figure out $$5^0$$ by looking at other powers of 5. $$5^3$$ is 125, $$5^2$$ is 25, then $$5^1$$ is 5.”

1. What pattern do you notice?
2. If this pattern continues, what should be the value of $$5^0$$? Explain how you know.
3. If this pattern continues, what should be the value of $$5^{\text-1}$$? Explain how you know.

### Problem 2

Select all the expressions that are equivalent to $$4^{\text-3}$$.

A:

-12

B:

$$2^{\text-6}$$

C:

$$\frac{1}{4^3}$$

D:

$$\left(\frac{1}{4}\right) \boldcdot \left(\frac{1}{4}\right) \boldcdot \left(\frac{1}{4}\right)$$

E:

12

F:

$$(\text-4) \boldcdot (\text-4) \boldcdot (\text-4)$$

G:

$$\frac{8^{\text-1}}{2^2}$$

### Problem 3

Write each expression using a single exponent.

1. $$\frac{5^3}{5^6}$$
2. $$(14^3)^6$$
3. $$8^3 \boldcdot 8^6$$
4. $$\frac{16^6}{16^3}$$
5. $$(21^3)^{\text-6}$$

### Problem 4

Andre sets up a rain gauge to measure rainfall in his back yard. On Tuesday, it rains off and on all day.

• He starts at 10 a.m. with an empty gauge when it starts to rain.
• Two hours later, he checks, and the gauge has 2 cm of water in it.
• It starts raining even harder, and at 4 p.m., the rain stops, so Andre checks the rain gauge and finds it has 10 cm of water in it.
• While checking it, he accidentally knocks the rain gauge over and spills most of the water, leaving only 3 cm of water in the rain gauge.
• When he checks for the last time at 5 p.m., there is no change.

Graph A