Question

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

Explanation:

Step1: Simplify the coefficient

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

Step2: Simplify the x - terms

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

Step3: Simplify the y - terms

Using the same exponent rule $\frac{a^m}{a^n}=a^{m - n}$ for the y - terms, $\frac{y^3}{y^7}=y^{3 - 7}=y^{-4}$. Converting to positive exponents, $y^{-4}=\frac{1}{y^4}$.

Step4: Combine the results

Multiply the simplified coefficient, x - term, and y - term together. So we have $9\times\frac{1}{x^7}\times\frac{1}{y^4}=\frac{9}{x^7y^4}$.

Answer:

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