Question

\\(\frac{20x^{2}y^{6}}{2x^{2}y}\\)

Explanation:

Step1: Simplify Coefficients

Divide the coefficient 20 by 2: $\frac{20}{2} = 10$

Step2: Simplify \( x \)-terms

For \( x \)-terms, use the rule \( \frac{x^m}{x^n} = x^{m - n} \). Here, \( m = 2 \), \( n = 2 \), so \( \frac{x^2}{x^2} = x^{2 - 2} = x^0 = 1 \) (we can ignore \( x^0 \) as it's 1)

Step3: Simplify \( y \)-terms

For \( y \)-terms, use the same rule. \( m = 6 \), \( n = 1 \), so \( \frac{y^6}{y^1} = y^{6 - 1} = y^5 \)

Step4: Combine Results

Multiply the simplified coefficient, \( x \)-term result, and \( y \)-term result: \( 10 \times 1 \times y^5 = 10y^5 \)

Answer:

\( 10y^5 \)