Question

using only positive expon
\\(\frac{15x^5y^2}{25x^2y}\\)

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{15}{25} \). We can divide both numerator and denominator by their greatest common divisor, which is 5. So \( \frac{15\div5}{25\div5}=\frac{3}{5} \).

Step2: Simplify \( x \)-terms

For the \( x \)-terms, we use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \). Here, \( a = x \), \( m = 5 \), and \( n = 2 \). So \( \frac{x^5}{x^2}=x^{5 - 2}=x^3 \).

Step3: Simplify \( y \)-terms

For the \( y \)-terms, again use the quotient rule of exponents. Here, \( a = y \), \( m = 2 \), and \( n = 1 \) (since \( y = y^1 \)). So \( \frac{y^2}{y^1}=y^{2 - 1}=y^1 = y \).

Step4: Combine all simplified terms

Multiply the simplified coefficient, \( x \)-term, and \( y \)-term together. So we get \( \frac{3}{5}x^3y \).

Answer:

\(\frac{3}{5}x^{3}y\)