Solving powers with the same exponent

1. PROBLEM:
A forest has deer. They live in
groups of .
How many groups of deer live in the
forest?
How did you find out?
ANSWER:
𝟔 𝟓 ÷ 𝟐 𝟓
= (𝟔 × 𝟔 × 𝟔 × 𝟔 × 𝟔 × 𝟔) ÷ (𝟐 × 𝟐 × 𝟐 × 𝟐 × 𝟐 × 𝟐)
=
𝟔 𝟓
𝟐 𝟓 = 𝟑 𝟓
= 𝟐𝟒𝟑 groups of deer in the forest

2. AIM
Today we will find
the product and
quotient of
numbers with
different bases
but the same
exponent.

3. MULTIPLYING POWERS WITH
THE SAME EXPONENTS
When two numbers that have different
bases but the same power are
multiplied, the product has a base equal
to the product of the two bases and a
power that is the common exponent. For
any non-zero integers a and b, and whole
number m:
𝒂 𝒎
× 𝒃 𝒎
= 𝒂 × 𝒃 𝒎

4. DIVIDING POWERS WITH THE
SAME EXPONENTS
In division involving two numbers with
different bases but the same power, the
power of the quotient is given by the
difference of the powers of the dividend
and the divisor. For any non-zero
integers a and b, and whole number m:
𝒂 𝒎
÷ 𝒃 𝒎
=
𝒂
𝒃
𝒎
= 𝒂 ÷ 𝒃 𝒎

5. EXAMPLE:
Simplify using the laws of
exponents.

6. T A S K :
Complete the table and compare the
answers of the two methods.
Number 1
(N1)
Number 2
(N2)
Multiplying
Using
Expanded
Form
Product by
Multiplying
the Bases
Divide
Using
Expanded
Form
Quotient
by
Dividing
the Bases
A.
B.

7. ANOTHER EXAMPLE:
Solve using the laws of
exponents.

8. FINISH S2
on page 15 of
your
Workbook.
CLASS WORK:

9. Complete
Practice Questions
#s 1 – 3, page 93 – 94
from the XSEED
Content Book.
HOMEWORK: