Zero and negative exponents

About this lesson

Grade 8 › Exponents and scientific notation

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Zero and negative exponents

Warm-up

Three quick questions from earlier lessons.

Discover

103=100010^3 = 1000, 102=10010^2 = 100, 101=1010^1 = 10. Each step divides by 10. What comes next, 10010^0?

  1. 11
  2. 00

Key idea

Keep dividing to go below exponent 1.

For a≠0a \neq 0: a0=1a^0 = 1 and a−n=1ana^{-n} = \dfrac{1}{a^n}. The exponent rules still work with zero and negative exponents.

Worked example

2−32^{-3} and 105⋅10−210^5 \cdot 10^{-2}.

2−3=182^{-3} = \tfrac{1}{8}
One over 2³.
105⋅10−2=10310^5 \cdot 10^{-2} = 10^3
5 + (−2).

Your turn, guided

Your turn: 10−210^{-2} as a fraction.

1100\tfrac{1}{100}
1/10².

Practice ★

  1. Write 5−15^{-1} as a fraction.
  2. Write 4−14^{-1} as a fraction.
  1. What is 51051^0?

Watch out!

Practice ★★

  1. 106⋅10−9=10?10^{ 6 } \cdot 10^{-9} = 10^{?}. What is the exponent?
  2. 108⋅10−9=10?10^{ 8 } \cdot 10^{-9} = 10^{?}. What is the exponent?

Exit ticket

Three questions to check you have got it.

  1. Write 5−15^{-1} as a fraction.
  2. Write 4−14^{-1} as a fraction.
  3. Write 2−12^{-1} as a fraction.

Summary card

Zero and negative exponents

a0=1a^0 = 1; a−n=1/ana^{-n} = 1/a^n.

Watch out: negative exponent, small positive number.

End of the lesson

Next lesson: Scientific notation Back to the chapter

Answers: Zero and negative exponents

A

  1. 15\frac{1}{5}
  2. 14\frac{1}{4}

B

  1. 11

C

  1. −3-3
  2. −1-1

D

  1. 15\frac{1}{5}
  2. 14\frac{1}{4}
  3. 12\frac{1}{2}

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