CPA EXPONENTS :GRADE 7
Product of Powers Property
ESSENTIAL QUESTION : How can you use inductive reasoning to observe patterns and write
general rules involving properties of exponents?
Activity 1: Finding Products of Powers
a) Copy and complete the table given below
b) Inductive Reasoning: Describe the pattern in the table.
Then write a general rule for multiplying two powers that have the same base.
𝑎𝑚 × 𝑎𝑛 = 𝑎
c) Use your rule to simplify the products in the first column of the table above. Does your rule
give the results in the third column?
Activity 2: Writing a Rule for Powers of Powers
Work with a partner. Write the expression as a single power. Then write a general rule for finding a
power of a power.
Write a general rule for determining the powers of powers
{(𝑎)𝑚 }𝑛 =𝑎
ACTIVITY 3: Writing a Rule for Powers of Products
Work with a partner. Write the expression as the product of two powers. Then write a general rule
for finding a power of a product.
The general rule for finding a product of a power is
(𝑎 × 𝑏)𝑚 = 𝑎 × 𝑏
Quotient of Powers Property
ESSENTIAL QUESTION : How can you divide two powers that have the same base?
Activity 4: Finding Quotients of Powers
Work with a partner.
a. Copy and complete the table.
b. INDUCTIVE REASONING
Describe the pattern in the table.
Then write a rule for dividing two powers that have the same base.
𝑎𝑚 ÷ 𝑎𝑛 = 𝑎
c.
Use your rule to simplify the quotients in the first column of the table above. Does your rule give
the results in the third column?
Zero and Negative Exponents
ESSENTIAL QUESTION : How can you evaluate a nonzero number with an exponent of zero?
How can you evaluate a nonzero number with a negative integer exponent?
ACTIVITY 5: Using the Quotient of Powers Property
Work with a partner.
a. Copy and complete the table.
b. REPEATED REASONING
Evaluate each expression in the first column of the table. What do you notice?
c.
How can you use these results to define 𝑎0 where a ≠ 0?