Question

Use the expression \(\frac{5^{2}}{5^{2}}\) to demonstrate the power of zero rule of exponents

Answer 1

The expression \(\frac{5^{2}}{5^{2}}\) can be used to demonstrate the power of zero rule of exponents, which states that any non-zero number raised to the power of zero is equal to 1.

Let's simplify the expression:

\[
\frac{5^{2}}{5^{2}} = 1
\]

This is true because any number divided by itself (as long as it is not zero) equals 1.

Now, using the properties of exponents, we can rewrite the expression:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

In this case, \(a = 5\), \(m = 2\), and \(n = 2\). Applying this property:

\[
\frac{5^{2}}{5^{2}} = 5^{2-2} = 5^{0}
\]

Since we already established \(\frac{5^{2}}{5^{2}} = 1\), we can set this equal to what we derived:

\[
5^{0} = 1
\]

This shows that \(5^{0} = 1\), thereby confirming the power of zero rule of exponents: any non-zero base raised to the power of zero is equal to 1.