Question

fully simplify using only positive exponents.\\(
\frac{27xy^{3}}{3x^{8}y^{7}}
\\)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 27 by 3: $\frac{27}{3} = 9$

Step2: Simplify the x - term

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the x - terms: $\frac{x}{x^8}=x^{1-8}=x^{-7}$. Since we need positive exponents, $x^{-7}=\frac{1}{x^7}$

Step3: Simplify the y - term

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the y - terms: $\frac{y^3}{y^7}=y^{3 - 7}=y^{-4}$. Since we need positive exponents, $y^{-4}=\frac{1}{y^4}$

Step4: Combine the results

Multiply the coefficient, the x - term, and the y - term together: $9\times\frac{1}{x^7}\times\frac{1}{y^4}=\frac{9}{x^7y^4}$

Answer:

$\frac{9}{x^{7}y^{4}}$