Question

1. \\(\frac{50y^2}{40y^3}\\) =

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{50}{40} \) by dividing numerator and denominator by their greatest common divisor, which is 10.
\( \frac{50\div10}{40\div10}=\frac{5}{4} \)

Step2: Simplify variables using exponent rule

For the variable part \( \frac{y^{2}}{y^{3}} \), use the exponent rule \( \frac{a^{m}}{a^{n}} = a^{m - n} \) (where \( a = y \), \( m = 2 \), \( n = 3 \)).
\( \frac{y^{2}}{y^{3}}=y^{2 - 3}=y^{-1}=\frac{1}{y} \) (since \( a^{-n}=\frac{1}{a^{n}} \))

Step3: Multiply the simplified parts

Multiply the simplified coefficient part and the simplified variable part:
\( \frac{5}{4}\times\frac{1}{y}=\frac{5}{4y} \)

Answer:

\( \frac{5}{4y} \)