7th Grade Math

Monomials

PART A BC

4

Multi-Part

Lesson

Get ConnectED

GLE 0706.3.1

Recognize and generate

equivalent forms for simple

algebraic expressions.

SPI 0706.2.1 Simplify

numerical expressions

involving rational numbers.

176 Rational Numbers

Multiply and Divide Monomials

EARTHQUAKES For each increase on the Richter scale, an

earthquake’s vibrations, or seismic waves, are 10 times greater. So, an

earthquake of magnitude 4 has seismic waves that are 10 times

greater than that of a magnitude 3 earthquake.

Richter

Scale

Times Greater than

Magnitude 3 Earthquake

Written Using

Powers

4 10 × 1 = 10 101

5 10 × 10 = 100 101 × 101 = 102

6 10 × 100 = 1,000 101 × 102 = 103

7 10 × 1,000 = 10,000 101 × 103 = 104

8 10 × 10,000 = 100,000 101 × 104 = 105

1. Examine the exponents of the powers in the last column. What do
   you observe?


2. MAKE A CONJECTURE Write a rule for determining the exponent of
   the product when you multiply powers with the same base. Test
   your rule by multiplying 2^2 and 2^4 using a calculator.

Recall that exponents are used to show repeated multiplication. You

can use the definition of an exponent to find a rule for multiplying

powers with the same base.

·····=(()·)

3 factors 4 factors

7 factors

·

=

Notice the sum of the original exponents is the exponent in the final

product.

Product of Powers

Words To multiply powers with the same base, add their

exponents.

Symbols am · an = am^ +^ n

Example 32 · 34 = 32 +^4 or 3^6

earthq

Main Idea

Multiply and divide

monomials.

Vocabulary

monomial

V

m

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