Question

divide using the quotient rule:
\frac{25 x^{11} y^{10}}{5 x y^{6}}=
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Explanation:

Step1: Divide the coefficients

The coefficient of the numerator is \(25\) and the coefficient of the denominator is \(5\). So, \(\frac{25}{5}=5\).

Step2: Apply the quotient rule for \(x\) - terms

For the \(x\) - terms, we have \(x^{11}\) in the numerator and \(x\) (which is \(x^{1}\)) in the denominator. Using the quotient rule \(a^{m}\div a^{n}=a^{m - n}\), we get \(x^{11-1}=x^{10}\).

Step3: Apply the quotient rule for \(y\) - terms

For the \(y\) - terms, we have \(y^{10}\) in the numerator and \(y^{6}\) in the denominator. Using the quotient rule \(a^{m}\div a^{n}=a^{m - n}\), we get \(y^{10 - 6}=y^{4}\).

Answer:

\(5x^{10}y^{4}\)