Question

How do I solve this question?

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \iff \sqrt[{ m}]{a^( n)} \\\\\\ \cfrac{a^{{ m}}}{a^{{ n}}}\implies \cfrac{a^{{ m}}}{1}\cdot \cfrac{1}{a^{{ n}}}\implies a^{{ m}}\cdot a^{-{ n}}\implies a^{{{ m}}{-{ n}}}\\\\ -----------------------------\\\\ thus \\\\\\ \cfrac{5√(x)}{20x^3}\implies \cfrac{5\sqrt[2]{x^1}}{20x^3}\implies \cfrac{5x^{(1)/(2)}}{20x^3}\implies \cfrac{5}{20x^3}\cdot \cfrac{x^{(1)/(2)}}{1} \\\\\\`



`\bf \cfrac{5}{20}\cdot \cfrac{1}{x^3}\cdot \cfrac{1}{x^{-(1)/(2)}}\implies \cfrac{1}{4}\cdot \cfrac{1}{x^3\cdot x^{-(1)/(2)}}\implies \cfrac{1}{4}\cdot \cfrac{1}{x^{3-(1)/(2)}} \\\\\\ \cfrac{1}{4}\cdot \cfrac{1}{x^{(5)/(2)}}\implies \cfrac{1}{4}\cdot \cfrac{1}{\sqrt[2]{x^5}}\implies \cfrac{1}{4√(x^5)}`