➕ Algebra 1 · Exponents and Polynomials
Zero and Negative Exponents flashcards
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All 13 flashcards at a glance
Card 1
What is x0 (for x ≠ 0)?
1. Any nonzero number to the power 0 is 1.
Card 2
What does a negative exponent mean?
x−n = 1/xn (for x ≠ 0): the reciprocal of the power with the positive exponent. It does not make the answer negative.
Card 3
Evaluate 10−4.
1/10000, or 0.0001. 10−4 = 1/104 = 1/10000.
Card 4
Evaluate 150.
1. The base does not matter, as long as it is not 0.
Card 5
Evaluate (−8)0 and −80.
(−8)0 = 1, but −80 = −(80) = −1. The parentheses decide what is raised to the 0 power.
Card 6
Write x−4 with a positive exponent (x ≠ 0).
1/x4
Card 7
Write 1/x6 using a negative exponent (x ≠ 0).
x−6
Card 8
Evaluate (1/4)−2.
16. Flip the fraction: (4/1)2 = 42 = 16.
Card 9
Simplify 9x0 and (9x)0 (with x ≠ 0).
9x0 = 9, because only x is raised to the 0 power. (9x)0 = 1, because the whole 9x is.
Card 10
Write 4y−3 with a positive exponent (y ≠ 0).
4/y3
Card 11
What is 00 in this course?
Undefined. The rule x0 = 1 needs x ≠ 0.
Card 12
Why do we define x0 to be 1?
x6 ÷ x6 = 1, because a nonzero number divided by itself is 1. The quotient rule would give x6−6 = x0. For the rule to keep working, x0 has to mean 1.
Card 13
What does a minus sign in an exponent tell you to do?
Take the reciprocal: flip the factor to the other side of the fraction bar. It does not make the number negative.