Question

select the equivalent expression.
\\(\frac{y}{x^5x^8y^{-5}}\\)
answer
\\(\frac{1}{x^3y^6}\\) \\(\frac{x^{13}}{y^6}\\) \\(\frac{y^6}{x^{13}}\\) \\(x^3y^6\\)

Explanation:

Step1: Simplify the x - terms

When multiplying variables with exponents, we add the exponents. For \(x^{5}x^{8}\), using the rule \(a^{m}\times a^{n}=a^{m + n}\), we have \(x^{5+8}=x^{13}\). So the denominator becomes \(x^{13}y^{-5}\) and the expression is \(\frac{y}{x^{13}y^{-5}}\).

Step2: Simplify the y - terms

Using the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\) for the y - terms. Here, the numerator is \(y^{1}\) and the denominator is \(y^{-5}\), so \(y^{1-(-5)}=y^{1 + 5}=y^{6}\).

Step3: Combine the results

After simplifying the x and y terms, we have \(\frac{y^{6}}{x^{13}}\).

Answer:

\(\frac{y^{6}}{x^{13}}\) (the option with \(\frac{y^{6}}{x^{13}}\))