Absolutely! Let's break down the given expression step-by-step to find the equivalent expression.
The original expression is:
[tex]$\frac{\left(x^6 y^8\right)^3}{x^2 y^2}$[/tex]
Step 1: Simplify the numerator
First, we need to simplify [tex]\(\left(x^6 y^8\right)^3\)[/tex]. When a term with a power is raised to another power, you multiply the exponents. Therefore:
[tex]$\left(x^6 y^8\right)^3 = x^{6 \cdot 3} y^{8 \cdot 3} = x^{18} y^{24}$[/tex]
Step 2: Write the entire expression with the simplified numerator
After simplifying the numerator, we get:
[tex]$\frac{x^{18} y^{24}}{x^2 y^2}$[/tex]
Step 3: Simplify the fraction
To simplify [tex]\(\frac{x^{18}}{x^2}\)[/tex], we subtract the exponent in the denominator from the exponent in the numerator:
[tex]$\frac{x^{18}}{x^2} = x^{18 - 2} = x^{16}$[/tex]
Similarly, to simplify [tex]\(\frac{y^{24}}{y^2}\)[/tex], we subtract the exponent in the denominator from the exponent in the numerator:
[tex]$\frac{y^{24}}{y^2} = y^{24 - 2} = y^{22}$[/tex]
Step 4: Combine the simplified terms
Combining the simplified terms, we get:
[tex]$x^{16} y^{22}$[/tex]
Thus, the expression equivalent to [tex]\(\frac{\left(x^6 y^8\right)^3}{x^2 y^2}\)[/tex] is:
[tex]$x^{16} y^{22}$[/tex]
This corresponds to the provided answer choice:
[tex]$\boxed{x^{16} y^{22}}$[/tex]
