4-16th 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 Exponents4³ 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 = 0.25Remember the rules

of multiplying decimals

b) 4² - 5 =4 · 4 – 5 =16 – 5 =11Remember 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

3) b x b x b x b x b

1) 2 x 2 x 2 = 4 x 2 = 8;2³

2) 0.8 x 0.8 x 0.8 x 0.8 = 0.64 x 0.64 = .4096;0.8⁴

3) b⁵

Try Some More!Evaluate.4) 7²

5) 6³

6) 0.5 ⁴

4) 7 x 7 = 49

5) 6 x 6 x 6 = 36 x 6 216

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 = 2 x 2 x 2 x 2 = 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 13-26

• Copy original problem first.

• Show all work!

• If time, work on Accelerated Math.