Solutions

1. 3 (Written Solution)

   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. y
3. 1 (Written Solution)

   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, \(\frac{7}{7}=1\) or \(\frac{\text{m}}{\text{m}}= 1\). Therefore, something like \(\frac{5^{1}}{5^{1}}=\frac{5}{5}=1\) since this is 5 divided by itself. Using the quotient rule, we also know that \(\frac{5^{1}}{5^{1}}=5^{(1-1)}=5^{0}\). The rest is a matter of logic. If \(\frac{5^{1}}{5^{1}}=1\) and \(\frac{5^{1}}{5^{1}} =5^{0}\), then \(5^{0} = 1\) as well.

4. 1
5. 1 (Solution Video | Transcript)
6. 1 (Solution Video | Transcript)