Question

simplify.
\frac{11sqrt{x^{9}}}{4sqrt{x^{3}}}
\frac{?}{x^{ }}

Explanation:

Step1: Use the rule of radicals $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$

$\frac{\sqrt[11]{x^{9}}}{\sqrt[4]{x^{3}}}=\frac{x^{\frac{9}{11}}}{x^{\frac{3}{4}}}$

Step2: Use the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$

$x^{\frac{9}{11}-\frac{3}{4}}$

Step3: Find a common - denominator for the exponents

The common denominator of 11 and 4 is 44. So $\frac{9}{11}-\frac{3}{4}=\frac{9\times4}{11\times4}-\frac{3\times11}{4\times11}=\frac{36}{44}-\frac{33}{44}=\frac{36 - 33}{44}=\frac{3}{44}$

Answer:

$x^{\frac{3}{44}}$