Question
Simplify to a single power of 4:
start fraction, 4, cubed, divided by, 4, squared, end fraction
start fraction, 4, cubed, divided by, 4, squared, end fraction
Answers
GPT-4o mini
To simplify the expression \(\frac{4^3}{4^2}\), you can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = 4\), \(m = 3\), and \(n = 2\). Applying the property gives:
\[
\frac{4^3}{4^2} = 4^{3-2} = 4^1
\]
Thus, the simplified expression is:
\[
4^1 = 4
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \(a = 4\), \(m = 3\), and \(n = 2\). Applying the property gives:
\[
\frac{4^3}{4^2} = 4^{3-2} = 4^1
\]
Thus, the simplified expression is:
\[
4^1 = 4
\]