Question

select the equivalent expression.
\\(\frac{x^3}{x^2 y^{-8} y^6}\\)
answer
\\(\frac{y^{14}}{x}\\) \\(\frac{1}{x y^2}\\)
\\(x y^2\\) \\(\frac{x}{y^{14}}\\)

Explanation:

Step1: Simplify the x - terms

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the x - terms in $\frac{x^{3}}{x^{2}y^{-8}y^{6}}$, we have $x^{3-2}=x^{1}=x$.

Step2: Simplify the y - terms

First, combine the y - terms in the denominator. Using the rule $a^m\times a^n=a^{m + n}$, for $y^{-8}y^{6}$, we get $y^{-8 + 6}=y^{-2}$. Then, using the rule $\frac{1}{a^{-n}}=a^{n}$, the expression becomes $\frac{1}{y^{-2}}=y^{2}$.

Step3: Combine the simplified x and y terms

Multiply the simplified x - term and y - term. We have $x\times y^{2}=xy^{2}$.

Answer:

\(xy^{2}\) (corresponding to the option " \(xy^{2}\) ")