Question

question
fully simplify using only positive exponents.
\\(\frac{25x^{5}y^{2}}{x^{8}y^{3}}\\)
answer

Explanation:

Step1: Simplify coefficient and x terms

For the coefficient, it remains 25. For the \(x\) terms, use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \), so \( \frac{x^5}{x^8}=x^{5 - 8}=x^{-3} \). By the negative exponent rule \( a^{-n}=\frac{1}{a^n} \), \( x^{-3}=\frac{1}{x^3} \).

Step2: Simplify y terms

For the \(y\) terms, use the quotient rule \( \frac{y^2}{y^3}=y^{2 - 3}=y^{-1} \). Using the negative exponent rule, \( y^{-1}=\frac{1}{y} \).

Step3: Combine all terms

Multiply the coefficient with the simplified \(x\) and \(y\) terms: \( 25\times\frac{1}{x^3}\times\frac{1}{y}=\frac{25}{x^3y} \).

Answer:

\(\frac{25}{x^{3}y}\)