Question

simplify.
\\(\frac{16y^2}{20y^5}\\)

Explanation:

Step1: Simplify the coefficients

First, simplify the fraction of the coefficients 16 and 20. The greatest common divisor of 16 and 20 is 4. So we divide both the numerator and the denominator by 4.
$\frac{16\div4}{20\div4} = \frac{4}{5}$

Step2: Simplify the variable terms

For the variable $y$, we use the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$ (where $a
eq0$). Here, $m = 2$ and $n = 5$, so $\frac{y^{2}}{y^{5}}=y^{2 - 5}=y^{- 3}=\frac{1}{y^{3}}$ (using the definition $a^{-n}=\frac{1}{a^{n}}$ for $a
eq0$).

Step3: Combine the simplified coefficient and variable terms

Multiply the simplified coefficient and the simplified variable term together: $\frac{4}{5}\times\frac{1}{y^{3}}=\frac{4}{5y^{3}}$

Answer:

$\frac{4}{5y^{3}}$