Question

simplify: \\(\frac{3a^5b^{-1}}{-3a^{-3}b^7}\\) = enter your answer with positive exponents.

Explanation:

Step1: Separate variables

$\frac{3x^3y^{-1}}{-6x^5y^{-3}} = \frac{3}{-6} \cdot \frac{x^3}{x^5} \cdot \frac{y^{-1}}{y^{-3}}$

Step2: Simplify coefficient

$\frac{3}{-6} = -\frac{1}{2}$

Step3: Simplify $x$-terms (exponent rule: $x^a/x^b=x^{a-b}$)

$\frac{x^3}{x^5} = x^{3-5} = x^{-2} = \frac{1}{x^2}$

Step4: Simplify $y$-terms (exponent rule: $y^a/y^b=y^{a-b}$)

$\frac{y^{-1}}{y^{-3}} = y^{-1-(-3)} = y^{2}$

Step5: Combine all parts

$-\frac{1}{2} \cdot \frac{1}{x^2} \cdot y^2 = \frac{y^2}{-2x^2}$

Answer:

$\frac{y^2}{-2x^2}$