Download Lesson 4-1a

4-1
6th grade math
Exponents
Objective
• To write and evaluate exponential expressions
• Why? To prepare you for higher learning in
math and science. To simplify factors. To
simplify prime factorization.
California State Standards
NS 1.3 (Gr.5): Understand and compute positive
integer powers of non-negative integers;
compute examples as repeated multiplication.
AF 1.2: Write and evaluate an algebraic expression
for a given situation, using up to three variables.
AF 1.4: Solve problems manually by using correct
order of operations or by using a scientific
calculator.
Vocabulary
• Exponent
– A number that tells how many times the base is used as a
factor
• 10⁴ = 10 x 10 x 10 x 10 = 10,000
– Exponent = 3, Base = 10
• Base
– The number that is multiplied by itself when raised to a power
• 5⁴ = 5 x 5 x 5 x 5 = 625. Base = 5
• Power
– The number of times a number is multiplied by itself.
• 4². It is read: 4 to the 2nd power. = 4 x 4 =16. 4 = Base. 2 = the
power.
• Exponential Expressions
– An expression written with exponents.
• 3 ⁴ = 3 · 3 · 3 · 3 = 81
More Vocabulary
• Integers
– A set of numbers
• …, -3, -2, -1, 0 , +1, +2, +3, …
• Variables
– A letter used to stand for a number in an expression or
equation
• 2x
• 4 + y = -10
• Order of Operations
– The order in which operations are done in calculations. Work
inside parentheses ( ) first. Then multiply and divide from left
to right. And finally add and subtract from left to right.
• 17 – (3 + 1) ÷ 2
• Evaluate
– Solve. Answer.
How to Solve Exponents
4³
1) Write out the product.
The base (bottom
integer) will be written
the number of times the
power (upper number)
indicates.
2) Count the number of
products to be sure that
you have enough. Group
together the pairs by
multiplying.
3) Solve, carefully.
4³
4·4·4=
↓↓ ↓
16 · 4
64
Other Examples
a) 0.5²
b) n² - 5, n = 4
a) 0.5² =
0.5 · 0.5 =
0.25
Remember the rules of
multiplying decimals
b) 4² - 5 =
4 ·4–5=
16 – 5 =
11
Remember the rules of
order of operations
Try It!
Use exponents to write each
expression.
1) 2 x 2 x 2
2) 0.8 x 0.8 x 0.8 x 0.8
1) 2 x 2 x 2 =
4 x2=
8;
2³
2) 0.8 x 0.8 x 0.8 x 0.8 =
0.64 x 0.64 =
.4096;
0.8⁴
3) b x b x b x b x b
3) b⁵
Try Some More!
Evaluate.
4) 7²
4) 7 x 7 =
49
5) 6³
5) 6 x 6 x 6 =
36 x 6
216
6) 0.5 ⁴
6) 0.5 x 0.5 x 0.5 x 0.5 =
0.25
x
0.25
0.0625
Even More!
Evaluate each expression
when n = 5
9) n² - 2
10) (n-3)⁴
11) 2n²
9) 5² - 2 =
25 -2 =
23
10) (5-3)⁴ =
(2)⁴ =
2x2x2x2=
4 x 4=
16
11) 2 · 5² =
2·5·5=
10 · 5 =
50
Objective Review
• To write and evaluate
exponential expressions
Why? You are more prepared
for higher learning in math
and science. Yow can
simplify factors. You can
simplify prime factorization.
Independent Practice
• Complete problems 1326
• Copy original problem
first.
• Show all work!
• If time, work on
Accelerated Math.