Lesson 1

Properties of Exponents

Problem 1

Find the value of each variable that makes the equation true.

1. $$2^5 \boldcdot 2^3 = 2^a$$
2. $$\frac{7^4}{7^b} = 7^{\text- 2}$$
3. $$8^c = \frac{1}{64}$$

Solution

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Problem 2

Select all the expressions equivalent to $$7^{\text- 2} \boldcdot 7^5 \boldcdot 7^{\text- 3}$$.

A:

$$0$$

B:

$$1$$

C:

$$\frac17$$

D:

$$7^0$$

E:

$$7^{10}$$

Solution

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Problem 3

Which expression is equal to $$\frac{3^8}{3^2}$$?

A:

$$1^6$$

B:

$$3^{\text- 6}$$

C:

$$3^4$$

D:

$$3^6$$

Solution

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Problem 4

Find the value of each variable that makes the equation true.

1. $$\frac{5^6}{5^m} = 5^9$$
2. $$2^3 \boldcdot 4^n = 2^{11}$$
3. $$(7^4)^k = 7^{\text-8}$$

Solution

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Problem 5

1. Evaluate the expression $$\frac{6^3}{6^3}$$.
2. Explain how this helps show why $$6^0 = 1$$.

Solution

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