Question

(05.02 MC) What is the simplified form of 15 x to the fifth power over 24 y to the eighth power divided by 4 x squared over 8 y to the fourth power

4 y cubed over 5 x to the fourth power
4 y to the fourth power over 5 x cubed
5 x to the fourth power over 4 y cubed
5 x cubed over 4 y to the fourth power

Answer 1

`\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^(-n) \qquad \qquad a^n\implies \cfrac{1}{a^(-n)} \\\\ -------------------------------\\\\ \cfrac{\quad (15x^5)/(24y^8)\quad }{(4x^2)/(8y^4)}\implies \cfrac{15x^5}{24y^8}\cdot \cfrac{8y^4}{4x^2}\implies \cfrac{120x^5y^4}{96y^8x^2}\implies \cfrac{120}{96}\cdot \cfrac{x^5x^(-2)}{y^8y^(-4)} \\\\\\ \cfrac{5}{4}\cdot \cfrac{x^(5-2)}{y^(8-4)}\implies \cfrac{5x^3}{4y^4}`