Zero & Negative Exponents 8.1 Zero & Negative Exponents

8.1 – Zero & Negative Exponents Goals / “I can…” Simplify expressions with zero and negative exponents Evaluate exponential expressions

Multiply Integers REVIEW 8.1 – Zero & Negative Exponents Multiply Integers REVIEW 1 • 1 = +1 1 • -1 = -1 -1 • -1 = +1 -1 • -1 • -1 = -1 -1 • -1 • -1 • -1 = +1 -1 • -1 • -1 • -1 • -1 = -1 -1 • -1 • -1 • -1 • -1 • -1 = +1 Odd # of Negatives = Negative Even # of Negatives = Positive

8.1 – Zero & Negative Exponents 22 Means… 2 • 2 = 4 21 Means… 2 = 2 20 Means… 1 What does 2-1 Mean?

8.1 – Zero & Negative Exponents What does 2-1 Mean? You cannot leave an exponent negative because there is NO WAY to express it’s meaning. You must make it positive!

8.1 – Zero & Negative Exponents You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals. If the negative exponent is on top, move it to the bottom.

8.1 – Zero & Negative Exponents Definition of Negative Exponent For any integer n, a-n is the reciprocal of an

a-n is the reciprocal of an 8.1 – Zero & Negative Exponents Definition of Negative Exponent For any integer n, a-n is the reciprocal of an

a-n is the reciprocal of an 8.1 – Zero & Negative Exponents Definition of Negative Exponent For any integer n, a-n is the reciprocal of an

8.1 – Zero & Negative Exponents A negative exponent is an inverse! Flip the number over to make the exponent positive! Simplify.

8.1 – Zero & Negative Exponents Follow the Pattern! 1 10 10 -1 1 10 = 0.1 10 1 2 100 3 -2 1 10 1 100 = 0.01 1,000 10 2 4 10,000 -3 1 10 1 1000 = 0.001 10 5 100,000 3

8.1 – Zero & Negative Exponents Zero Exponent: Negative Exponent: RULE: YOU SHOULD NEVER HAVE A NEGATIVE EXPONENT AS YOUR FINAL ANSWER

8.1 – Zero & Negative Exponents Simplify.

8.1 – Zero & Negative Exponents Simplify the following: a. 3 c. (-4) b. (-8.1) d. (2.45678913) -2 -5

8.1 – Zero & Negative Exponents Simplify.

8.1 – Zero & Negative Exponents Simplify a. 11m b. 7s - 4t c. d. -5 2

Simplify the following expressions: 1 x5 16 -n3p6 1

Practice Problems 1. 2-2 2. (-2)0 3. 5-x 4. (½)-1 5. 5(2-1) 6. 2x-2y-3 1. 2-2 ¼ 2. (-2)0 1 3. 5-x 1/5x 4. (½)-1 2 5. 5(2-1) 5/2 6. 2x-2y-3 2/y3x2

More Practice 7. x-5 1/x5 8. x5/2 9. x4y-7 x4/y7 10. x3y/9

8.1 – Zero & Negative Exponents Evaluate each expression for n = -2 and w = 5 a. n w b. c. d. -3