Question

fully simplify using only positive exponents. \\(\frac{125x^{3}y^{6}}{xy^{4}}\\)

Explanation:

Step1: Simplify the coefficient and variables separately

For the coefficient: \(125\) remains as is. For the \(x\) terms: use the quotient rule of exponents \( \frac{x^m}{x^n}=x^{m - n}\), so \( \frac{x^3}{x}=x^{3 - 1}=x^2\). For the \(y\) terms: \( \frac{y^6}{y^4}=y^{6 - 4}=y^2\).

Step2: Combine the simplified parts

Multiply the simplified coefficient, \(x\) term, and \(y\) term together: \(125\times x^2\times y^2 = 125x^2y^2\).

Answer:

\(125x^2y^2\)