What does it mean to have powers of 0 or 1? We can use the rules we’ve been learning to discover what these mean.

Video Source (04:16 mins) | Transcript

Any number to the 1 power is just itself and any number to the 0 power is 1. Remember that the only exception to this rule is 0 raised to the 0 power.

Additional Resources

• Khan Academy: The 0 & 1st Power (05:06 mins, Transcript)

Practice Problems

1. \(3^{1}=?\) (
   Solution

   x

   Solution:
   3
   Details:
   Any number raised to the power of 1 is still itself, so \(3^{1}\) is just 3.
   
   This is because the exponent means the number of 3’s being multiplied together.
   )
2. \({\text{y}}^{1}=?\) (
   Solution

   x

   Solution:
   y
   )
3. \(5^{0}=?\) (
   Solution

   x

   Solution:
   1
   Details:
   Any number raised to the power of 0 is 1.
   
   The following explains why:
   
   We can prove this using what we know about division and the quotient rule. First, we know that anything divided by itself equals 1. For example, \(\dfrac{7}{7}=1\) or \(\dfrac{\text{m}}{\text{m}}= 1\). Therefore, something like \(\dfrac{5^{1}}{5^{1}}=\dfrac{5}{5}=1\) since this is 5 divided by itself. Using the quotient rule, we also know that \(\dfrac{5^{1}}{5^{1}}=5^{(1-1)}=5^{0}\). The rest is a matter of logic. If \(\dfrac{5^{1}}{5^{1}}=1\) and \(\dfrac{5^{1}}{5^{1}} =5^{0}\), then \(5^{0} = 1\) as well.
   )
4. \({\text{b}}^{0}=?\) (
   Solution

   x

   Solution:
   1
   )
5. \(6^{(8-8)}=?\) (
   Video Solution

   x

   Solution:
   1
   Details:
   

   
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   )
6. \(\dfrac{{\text{x}}^{9}}{{\text{x}}^{9}}=?\) (
   Video Solution

   x

   Solution:
   1
   Details:
   

   
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