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Zero &
Negative
Exponents
Zero exponent
• For any nonzero number a, a0
= 1
• 50
= 1
• (-2)0
= 1
• (2/3)0
= 1
• 1.020
= 1
• - 80
= -1
Evaluate the function
• For t = 0
• f(t) = 1000 ⋅ 2 t
• Substitute 0 in for t
• We know that 2 0
= 1
• So the function = 1...
Negative exponents
• For any nonzero number a and any
integer n, a–n
= 1/an
• & 1/a–n
= an
• 6–4
= 1/64
• 7–1
= 1/71
Write as a simple fraction
• 4–3
• 1/43
• 1/64
• (-3)–2
• 1/ (-3)2
• 1/9
Rewrite each so that all
exponents are positive
• Exponents only go with the variable
directly in front of it!
• 4yx–3
• 4...
Graph the function over
the domain -2 ≤ x ≤ 2
• Set your calculator margins so that
you have an x minimum of -2 and
an x m...
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Zero & Negative Exponents

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Zero & Negative Exponents

  1. 1. Zero & Negative Exponents
  2. 2. Zero exponent • For any nonzero number a, a0 = 1 • 50 = 1 • (-2)0 = 1 • (2/3)0 = 1 • 1.020 = 1 • - 80 = -1
  3. 3. Evaluate the function • For t = 0 • f(t) = 1000 ⋅ 2 t • Substitute 0 in for t • We know that 2 0 = 1 • So the function = 1000
  4. 4. Negative exponents • For any nonzero number a and any integer n, a–n = 1/an • & 1/a–n = an • 6–4 = 1/64 • 7–1 = 1/71
  5. 5. Write as a simple fraction • 4–3 • 1/43 • 1/64 • (-3)–2 • 1/ (-3)2 • 1/9
  6. 6. Rewrite each so that all exponents are positive • Exponents only go with the variable directly in front of it! • 4yx–3 • 4y(1/x3 ) • 4y/x3 • 1/w –4 • 1⋅ w4 • w4
  7. 7. Graph the function over the domain -2 ≤ x ≤ 2 • Set your calculator margins so that you have an x minimum of -2 and an x maximum of 2. • Leave the y at -10 and 10. • Sketch each graph as you see it. • Pay attention to how each graph differs, and make note of why you think they differ.

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