Question

question
fully simplify using only positive exponents.
\\(\frac{3x^{6}y^{3}}{x^{2}y^{7}}\\)

Explanation:

Step 1: Simplify the coefficient and \(x\)-terms

For the \(x\)-terms, use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \). So, \( \frac{x^6}{x^2}=x^{6 - 2}=x^4 \). The coefficient remains 3.

Step 2: Simplify the \(y\)-terms

For the \(y\)-terms, apply the quotient rule: \( \frac{y^3}{y^7}=y^{3 - 7}=y^{-4} \). But we need positive exponents, so \( y^{-4}=\frac{1}{y^4} \).

Step 3: Combine the results

Multiply the coefficient, \(x\)-term, and the simplified \(y\)-term. So we have \( 3\times x^4\times\frac{1}{y^4}=\frac{3x^4}{y^4} \).

Answer:

\(\dfrac{3x^4}{y^4}\)