Question

c) \\(dfrac{sqrt6{x^2}}{sqrt3{x^4}sqrt4{x^3}}\\)

Explanation:

Step1: Convert radicals to exponents

$\frac{x^{\frac{2}{6}}}{x^{\frac{4}{3}} \cdot x^{\frac{3}{4}}}$

Step2: Simplify exponents in numerator

$\frac{x^{\frac{1}{3}}}{x^{\frac{4}{3}} \cdot x^{\frac{3}{4}}}$

Step3: Combine exponents in denominator

$\frac{x^{\frac{1}{3}}}{x^{\frac{4}{3}+\frac{3}{4}}}$

Step4: Calculate denominator exponent sum

$\frac{x^{\frac{1}{3}}}{x^{\frac{16}{12}+\frac{9}{12}}} = \frac{x^{\frac{1}{3}}}{x^{\frac{25}{12}}}$

Step5: Subtract exponents (division rule)

$x^{\frac{1}{3}-\frac{25}{12}} = x^{\frac{4}{12}-\frac{25}{12}}$

Step6: Simplify final exponent

$x^{-\frac{21}{12}} = x^{-\frac{7}{4}}$

Answer:

$x^{-\frac{7}{4}}$ ou $\frac{1}{x^{\frac{7}{4}}}$