4-1 6 th 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. 4 ². It is read: 4 to the 2 nd 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 4³4³ 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. 4³4³ 4 · 4 · 4 = ↓↓ ↓ 16· 4 64

Other Examples a) 0.5 ² b) n² - 5, n = 4 a) 0.5 ² = 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 3)b x b x b x b x b 1) 2 x 2 x 2 = 4 x 2 = 8; 2³2³ 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) 7 ² 5) 6³ 6) 0.5 ⁴ 4) 7 x 7 = 49 5) 6 x 6 x 6 = 36 x ) 0.5 x 0.5 x 0.5 x 0.5 = 0.25 x

Even More! Evaluate each expression when n = 5 9) n ² ) (n-3) ⁴ 11) 2n² 9) 5 ² - 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 Copy original problem first. Show all work! If time, work on Accelerated Math.