Question

simplify.\\(\frac{45y^{6}}{27y^{2}}\\)

Explanation:

Step1: Simplify the numerical coefficients

Find the greatest common divisor of 45 and 27, which is 9. Divide both by 9:
$\frac{45 \div 9}{27 \div 9} = \frac{5}{3}$

Step2: Simplify the variable terms

Use the exponent rule $\frac{y^a}{y^b}=y^{a-b}$:
$y^{6-2}=y^4$

Step3: Combine the results

Multiply the simplified coefficient and variable term.

Answer:

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