Question

what does it mean to raise a number to the power of 0? you can look at patterns with exponents to find out. what is the value of $3^2$? $3^2 = \square$ \

$$\begin{tabular}{|c|c|} \\hline $3^n$ & value \\\\ \\hline $3^4$ & 81 \\\\ \\hline $3^3$ & 27 \\\\ \\hline $3^2$ &? \\\\ \\hline $3^1$ & \\\\ \\hline $3^0$ & \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Recall exponent rule

For a non - zero number \(a\) and positive integers \(m\) and \(n\), \(a^{m}\div a^{n}=a^{m - n}\). Also, we can observe the pattern of powers of 3. We know that \(3^{4}=81\), \(3^{3} = 27\). Notice that \(3^{4}\div3^{1}=3^{3}\), and \(81\div3 = 27\). In general, to find \(3^{n}\) from \(3^{n + 1}\), we divide by 3.

Step2: Calculate \(3^{2}\)

We know that \(3^{3}=27\). To find \(3^{2}\), we can use the rule \(3^{3}\div3^{1}=3^{3 - 1}=3^{2}\), or we can use the pattern. Since \(3^{3}=27\), and to get from \(3^{3}\) to \(3^{2}\), we divide by 3. So \(27\div3 = 9\). Also, by the definition of exponents, \(3^{2}=3\times3=9\).

Answer:

\(9\)