Question

Simplify 9y^7/15x^5•5x^2/45y^3

Answer 1

tell me
y^3/y=?

Answer 2

We know: \(\huge \color{red}{\frac{a^x}{a^y}=a^{x-y}}\)
\(\Large \frac{9y^7}{15x^5}\times \frac{5x^2}{45y^3}=\frac{9y^7}{45y^3}\times \frac{5x^2}{15x^5}\)
Now, tell me \(\Large \frac{9y^7}{45y^3}=?\) and \(\Large \frac{5x^2}{15x^5}=?\)

Answer 3

\(\Large \frac{9y^7}{45y^3}=\frac{9}{45}\times \frac{y^7}{y^3}=\frac{1}{5}\times y^{7-3}=\frac{y^4}{5}\)
\(\Large \frac{5x^2}{15x^5}=\frac{5}{15}\times \frac{x^2}{x^5}=\frac{1}{3}\times x^{2-5}=\frac{x^{-3}}{3}=\frac{1}{3x^3}\)
\(\Large \color{red}{(a^{-m}=\frac{1}{a^m} \Rightarrow x^{-3}=\frac{1}{x^3})}\)