Question
An expression is shown.
`\frac{5^{4}}{5^{2}}`
What is the value of the expression?
`\frac{5^{4}}{5^{2}}`
What is the value of the expression?
Answers
GPT-4o mini
To simplify the expression \(\frac{5^{4}}{5^{2}}\), we can use the properties of exponents. Specifically, when dividing exponential expressions with the same base, we subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, the base \(a\) is \(5\), \(m\) is \(4\), and \(n\) is \(2\). Applying the property:
\[
\frac{5^{4}}{5^{2}} = 5^{4-2} = 5^{2}
\]
Now, we calculate \(5^{2}\):
\[
5^{2} = 25
\]
Therefore, the value of the expression \(\frac{5^{4}}{5^{2}}\) is
\[
\boxed{25}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, the base \(a\) is \(5\), \(m\) is \(4\), and \(n\) is \(2\). Applying the property:
\[
\frac{5^{4}}{5^{2}} = 5^{4-2} = 5^{2}
\]
Now, we calculate \(5^{2}\):
\[
5^{2} = 25
\]
Therefore, the value of the expression \(\frac{5^{4}}{5^{2}}\) is
\[
\boxed{25}
\]