Sure. Let's simplify the expression:
[tex]\[
\frac{\left(x^{5 / 3} y^3\right)^2}{x^{4 / 3} y^2}
\][/tex]
Step-by-step solution:
1. First, simplify the numerator [tex]\(\left(x^{5 / 3} y^3\right)^2\)[/tex]:
[tex]\[
\left(x^{5 / 3} y^3\right)^2 = (x^{5 / 3})^2 \cdot (y^3)^2 = x^{(5 / 3) \cdot 2} \cdot y^{3 \cdot 2} = x^{10 / 3} \cdot y^6
\][/tex]
So, the numerator becomes:
[tex]\[
x^{10 / 3} \cdot y^6
\][/tex]
2. The denominator remains:
[tex]\[
x^{4 / 3} y^2
\][/tex]
3. Now, divide the simplified numerator by the simplified denominator:
[tex]\[
\frac{x^{10 / 3} \cdot y^6}{x^{4 / 3} y^2}
\][/tex]
4. To perform the division, subtract the exponents of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] independently:
For [tex]\(x\)[/tex]:
[tex]\[
x^{10 / 3} / x^{4 / 3} = x^{(10 / 3) - (4 / 3)} = x^{6 / 3} = x^2
\][/tex]
For [tex]\(y\)[/tex]:
[tex]\[
y^6 / y^2 = y^{6 - 2} = y^4
\][/tex]
So, the simplified expression becomes:
[tex]\[
x^2 \cdot y^4
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
x^2 y^4
\][/tex]
