Negative Exponents and Zero Exponents

Negative & Zero 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

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

Negative & Zero 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!

Negative & Zero 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.

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

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

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

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

Negative & Zero Exponents = 3 3 3 Follow the Pattern! = 3 3 Notice that anything to the zero power is always one! = 3 = 1 = = =

Negative & Zero 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

Negative & Zero Exponents Study the table and FOLLOW THE PATTERN! Exponent, n 25 24 23 22 21 20 2–1 2–2 2–3 Power, 2n 1 2 1 4 1 8 32 16 8 4 2 1 What do you think 2–4 will be? 2–4 = 1 = 1 24 16 What do you think 2–5 will be? 2–5 = 1 = 1 25 32

Negative & Zero Exponents Study the table and FOLLOW THE PATTERN! Exponent, n 35 34 33 32 31 30 3–1 3–2 3–3 Power, 3n 1 3 1 9 1 27 243 81 27 9 3 1 What do you think 3–4 will be? 3–4 = 1 = 1 34 81 What do you think 3–5 will be? 3–5 = 1 = 1 35 243

Negative & Zero Exponents Negative Exponent:

Negative & Zero Exponents Simplify.

Negative & Zero Exponents Simplify.

Negative & Zero Exponents Simplify.

Negative & Zero Exponents Identity Property Why It Works 2 -2 3 3 x0 = 1 9 9 = 1 Any number to the zero power is ALWAYS ONE.

Take Out Your Study Guide!!! Negative & Zero Exponents That's all Folks! That’s all folks Take Out Your Study Guide!!!

Powers of Ten # 4 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

Negative Exponents For any integer n, a-n is the reciprocal of an # 5 EXAMPLES: A negative exponent is an inverse!

Ex: # 6 Zero Exponent Any number to the zero power is ALWAYS ONE.