(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 :

[tex]\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 \frac{15x^5}{24y^8}\quad }{\frac{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}[/tex]