Question

question
fully simplify using only positive exponents.
\\(\frac{5x^{7}y^{5}}{10xy^{3}}\\)
answer attempt 1 out of 5

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{5}{10} \). We know that \( \frac{5}{10}=\frac{1}{2} \).

Step2: Simplify \( x \)-terms

For the \( x \)-terms, use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \). Here, \( \frac{x^{7}}{x^{1}}=x^{7-1}=x^{6} \) (since \( x = x^{1} \)).

Step3: Simplify \( y \)-terms

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

Step4: Combine all simplified terms

Multiply the simplified coefficient, \( x \)-term, and \( y \)-term together. We get \( \frac{1}{2}\times x^{6}\times y^{2}=\frac{x^{6}y^{2}}{2} \).

Answer:

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