Multiplying terms with exponents

Multiplying Terms with Exponents

Algebra 1A/Meredith Brown

3×3 = 9
7×7×7 = 343
10×10×10×10 = 10,000

Expanded form (we see the multiplication)

3² = 9

7³ = 343
10⁴ = 10,000

Exponent form

You already know about exponents with real number bases
Exponents (also called powers) are sometimes thought of as "repeat multiplication"

a×a
y×y×y
n×n×n×n

Expanded form (we see the multiplication)

a²
y³
n⁴

Exponent form

Logically, the same rules will apply when we have variables as bases
Exponents still represent "repeat multiplication"

3x3
(y×y×y) × (y×y)
(n×n×n×n) × (n×n×n×n×n)

Expanded form (we see the multiplication)

3¹×3¹
y³×y²
n⁴×n⁵

Exponent form

Multiplying same-base terms that have exponents
As the saying goes, "When in doubt, expand it out."

3x3 = 3² = 9
(y×y×y) × (y×y) = y⁵
(n×n×n×n) × (n×n×n×n×n) = n⁹

Expanded form (we see the multiplication)

3¹×3¹
y³×y²
n⁴×n⁵

Exponent form

So what does this all mean?
Let's take a look

Open Ended

What do you notice about the relationship between y³×y² and y⁵?

Or between n⁴×n⁵ and n⁹?

2³×2² = 2³⁺² = 2⁵

n⁴×n⁹ = n⁴⁺⁹ = n¹³
m²×mn³ cannot be combined into one term

If so, add the exponents!

2³×2² YES
n⁴×n⁹ YES
m²×mn³ NO

Do they have the same base?

How to multiply numbers with exponents that have the same base
Expanding it out does take a long time sometimes!

Fill in the Blank

Now try this one: What exponent goes where the ? is

b⁷ × b⁹ = b^?

Fill in the Blank

Now try this one: Write the exponent that goes where the ? is.

y³ × y⁷ × y² = y^?

Now, submit your notes on Schoology, including screenshots of your answers to the three question slides and complete the DeltaMath assignment.