Question

fully simplify using only positive exponents.\
\\(\frac{15x^{5}y^{2}}{25x^{2}y}\\)

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{15}{25} \) by dividing 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, use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \). Here, \( \frac{x^5}{x^2}=x^{5 - 2}=x^3 \).

Step3: Simplify \( y \)-terms

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

Step4: Combine results

Multiply the simplified coefficient, \( x \)-term, and \( y \)-term together: \( \frac{3}{5}\times x^3\times y=\frac{3x^3y}{5} \).

Answer:

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