Question

simplify.
\\(\frac{5x^{-8}y^{2}}{15y^{-1}x^{-7}}\\)
write your answer using only positive exponents.

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients: $\frac{5}{15}=\frac{1}{3}$

Step2: Simplify the \(x\)-terms

Use the rule \(a^m\div a^n = a^{m - n}\) for \(x\)-terms: \(x^{-8}\div x^{-7}=x^{-8-(-7)}=x^{-1}=\frac{1}{x}\)

Step3: Simplify the \(y\)-terms

Use the rule \(a^m\div a^n = a^{m - n}\) for \(y\)-terms: \(y^{2}\div y^{-1}=y^{2-(-1)}=y^{3}\)

Step4: Combine all parts

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term: \(\frac{1}{3}\times\frac{1}{x}\times y^{3}=\frac{y^{3}}{3x}\)

Answer:

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