Question

what does it mean to raise a number to the power of 0? you can look at patterns with exponents to find out. how do the exponents change from one row of the table to the next? to get to the next row of the table, decrease the exponent by 1. how do the values change from one row of the table to the next? to get to the next row of the table, divide the value by
3^n value
3^4 81
3^3 27
3^2 9
3^1 3
3^0 ?

Explanation:

Step1: Analyze the pattern of value - change

We know that $3^4 = 81$, $3^3=27$, $3^2 = 9$, $3^1=3$. To get from $3^4$ to $3^3$, we divide $81$ by $3$ to get $27$. To get from $3^3$ to $3^2$, we divide $27$ by $3$ to get $9$. To get from $3^2$ to $3^1$, we divide $9$ by $3$ to get $3$. So, to get to the next row of the table, we divide the value by $3$.

Step2: Calculate $3^0$

Since we divide by $3$ each time we decrease the exponent by $1$, when going from $3^1$ to $3^0$, we divide the value of $3^1$ (which is $3$) by $3$. So $3^0=\frac{3}{3}=1$.

Answer:

1