Question

question
fully simplify using only positive exponents.
\\(\frac{20x^{3}y^{5}}{50x^{2}y^{3}}\\)
answer
attempt 1 out of 2

Explanation:

Step1: Simplify the coefficients

First, simplify the fraction of the coefficients \( \frac{20}{50} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 10. So, \( \frac{20\div10}{50\div10}=\frac{2}{5} \).

Step2: Simplify the \( x \)-terms

For the \( x \)-terms, we use the rule of exponents \( \frac{x^m}{x^n}=x^{m - n} \). Here, we have \( \frac{x^3}{x^2} \), so \( x^{3-2}=x^1 = x \).

Step3: Simplify the \( y \)-terms

For the \( y \)-terms, we use the same exponent rule \( \frac{y^m}{y^n}=y^{m - n} \). Here, we have \( \frac{y^5}{y^3} \), so \( y^{5 - 3}=y^2 \).

Step4: Combine the simplified terms

Now, we multiply the simplified coefficient, \( x \)-term, and \( y \)-term together. So we get \( \frac{2}{5}\times x\times y^2=\frac{2xy^2}{5} \).

Answer:

\( \frac{2xy^2}{5} \)