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What are Exponents?

Definition: Exponents

Summary

  1. 'a' and 'b' are variables
  2. In the diagram, b is the exponent, also called a power
  3. When we raise 'a' to the 'b' power, we multiply 'a' by itself 'b' times
  4. So 24 is just 2 multiplied by itself 4 times
  5. (-2)3 = (-2)•(-2)•(-2) = -8
  6. If the power is negative, you can put the whole thing on the bottom of a fraction and make the exponent positive
  7. Anything raise to the 1st power is itself
  8. Anything raised to the 0 power is 1

Notes

    1. 'a' and 'b' are variables
    1. 'b' is a variable
    1. 'b' is a variable
    1. 'a' and 'b' are variables
    1. This is what we mean when we say 'raise a to the b power'
    2. 'a' and 'b' are variables
    1. Exponents can be either positive or negative, just like normal numbers
    1. 'b' is a variable
    1. 2 is our 'a' and 4 is our 'b' in this example
    2. 'a' and 'b' are variables
    1. 2 is our 'a' and 4 is our 'b' in this example
    2. 'a' and 'b' are variables
    1. 24 = 2•2•2•2 = 16
    2. 2 is our 'a' and 4 is our 'b' in this example
    3. 'a' and 'b' are variables
    1. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b' our power
    2. 'a' is a variable
    1. -2 is our 'a' and 3 is our 'b' in this example
    2. 'a' and 'b' are variables
    1. When we raise -2 to the 3rd power, we multiply -2 by itself 3 times
    2. (-2)3 = (-2)•(-2)•(-2)
    1. (-2)3 = (-2)•(-2)•(-2)
    1. First we multiplied the numbers together, 2•2•2=8, and now we are multiplying the signs together
    1. First we multiplied the numbers together, 2•2•2=8, and now we are multiplying the signs together
    1. (-2)•(-2)•(-2) = -8
    1. As long as 'b' is positive, the rule is the same for whatever 'a' that is in our equation ab
    2. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b', our power
    3. 'a' and 'b' are variables
    1. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b', our power
    2. 'a' and 'b' are variables
    1. 'x' and 'y' are variables
    1. As long as 'b' is positive, the rule is the same for whatever 'a' that is in our equation ab
    2. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b', our power
    1. Raising something to a power is the same thing as raising something to an exponent
    1. 'b' is our exponent, or power
    2. 'b' is a variable
    1. 2 is our 'a' and -4 is our 'b' in this example
    2. 'a' and 'b' are variables
    1. So we would put 2-4 on the bottom of a fraction, and switch the -4 to a positive 4
    2. The top of the fraction is 1
    1. Doing 24 is raising 'a' to a positive 'b', which we already know who to do
    2. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b' our power
    3. 'a' and 'b' are variables
    1. So a-b = 1/ab
    2. 'a' and 'b' are variables
    1. So we would put (-2)-3 on the bottom of a fraction, and switch the -3 to a positive 3
    1. So a-b = 1/ab
    2. 'a' and 'b' are variables
    1. You just take the value we have for 'a', and multiply it by itself a number of times equal to 'b' our power
    2. Since b=1, a1 is just 'a'
    3. 'a' and 'b' are variables
    1. Since b=1, a1 is just 'a'
    2. 'a' and 'b' are variables