Question

8.5 divide radical expressions (homework) score: 2/14 answered: 2/14 question 3 simplify (\frac{sqrt{81x^{11}}}{sqrt{y^{11}}}=)

Explanation:

Step1: Use quotient - rule of radicals

$\frac{\sqrt{81x^{11}}}{\sqrt{y^{11}}}=\sqrt{\frac{81x^{11}}{y^{11}}}$

Step2: Simplify the constant and variables separately

We know that $\sqrt{81} = 9$. Also, for the variables, using the rule $\sqrt{\frac{a^m}{b^m}}=\frac{\sqrt{a^m}}{\sqrt{b^m}}$ and $\sqrt{a^m}=a^{\frac{m}{2}}$, we have $\sqrt{\frac{x^{11}}{y^{11}}}=\frac{x^{\frac{11}{2}}}{y^{\frac{11}{2}}}$. So the expression becomes $9\frac{x^{\frac{11}{2}}}{y^{\frac{11}{2}}}$

Answer:

$9\frac{x^{\frac{11}{2}}}{y^{\frac{11}{2}}}$