Certainly! Let's simplify the given expression step by step.
We start with the expression:
[tex]\[
\frac{3 x^3}{3 x y^3}
\][/tex]
Step 1: Observe that both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) have a common factor of 3. We can simplify this by canceling out the common factor of 3 from both the numerator and the denominator.
So we have:
[tex]\[
\frac{3 x^3}{3 x y^3} = \frac{x^3}{x y^3}
\][/tex]
Step 2: Now, look at the remaining expression [tex]\(\frac{x^3}{x y^3}\)[/tex]. Notice that both the numerator and the denominator have the variable [tex]\(x\)[/tex]. We can simplify this part by canceling out one [tex]\(x\)[/tex] from both the numerator and the denominator since [tex]\(x = x^1\)[/tex].
[tex]\[
\frac{x^3}{x y^3} = \frac{x^{3-1}}{y^3} = \frac{x^2}{y^3}
\][/tex]
Where we subtracted the exponents of [tex]\(x\)[/tex] in the numerator and denominator using the property of exponents [tex]\(\frac{x^a}{x^b} = x^{a-b}\)[/tex].
Final simplified expression:
[tex]\[
\frac{x^2}{y^3}
\][/tex]
Thus, the simplified form of the given expression [tex]\(\frac{3 x^3}{3 x y^3}\)[/tex] is:
[tex]\[
\frac{x^2}{y^3}
\][/tex]
