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Simplifying Negative and Zero Exponents

Learn how to simplify expressions with negative and zero exponents, avoiding negative exponents in your answer. Understand the concept and application through clear examples and follow the patterns provided in the study table.

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Simplifying Negative and Zero Exponents

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  1. Negative Exponents and Zero Exponents

  2. 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

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

  4. Negative & Zero Exponents • What does 2-1 Mean? • You cannotleave an exponent negative because there is no way to express it’s meaning. • You must make it positive!

  5. 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.

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

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

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

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

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

  11. Negative & Zero Exponents Follow the Pattern! 1 10 10 10 10 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

  12. 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 2416 What do you think 2–5 will be? 2–5 = 1 = 1 2532

  13. 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 3481 What do you think 3–5 will be? 3–5 = 1 = 1 35243

  14. Negative & Zero Exponents • Zero Exponent: • Negative Exponent:

  15. Negative & Zero Exponents Simplify.

  16. Negative & Zero Exponents Simplify.

  17. Negative & Zero Exponents Simplify.

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

  19. # 4 Powers of Ten • 1 • 10 • 10 • 10 • 10 • 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

  20. # 5 Negative Exponents • For any integer n, a-n is the • reciprocal of an • EXAMPLES: • A negative exponent is an inverse!

  21. # 6 Zero Exponent • Any number to the zero power is ALWAYS ONE. • x0 = 1 • Ex:

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