The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, [tex] 3^{-2} = \frac{1}{3^{2} } [/tex].
Also remember that the zero exponent rule says that any number raised to zero is 1. For example, [tex] 3^{0} = 1[/tex].
Back to the Problem:
To fill out the table, you want to plug in the x-values you're given in the first row into [tex]y = 7^x[/tex] to get the y-values in order to fill in the second row.
The missing y-values are for when x = -2, x = 0, and x = 2.
Find x = -2. Use the negative exponent rule:
[tex]y = 7^x\\
y = 7^{-2}\\
y = \frac{1}{7^{2}} \\
y = \frac{1}{49}[/tex]
Find x = 0. Use the zero exponent rule:
[tex]y = 7^x\\
y = 7^{0}\\
y = 1[/tex]
Find x = 2.
[tex]y = 7^x\\
y = 7^{2}\\
y = 49[/tex]
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Answer: Your blanks from left to right are 49, 1, 49.
