Question

ositive exponents.
\frac{18x^{7}y^{7}}{30x^{5}y^{6}}

Explanation:

Step1: Simplify the coefficients

First, simplify the fraction of the coefficients 18 and 30. Find the greatest common divisor (GCD) of 18 and 30, which is 6. Divide both 18 and 30 by 6: $\frac{18\div6}{30\div6}=\frac{3}{5}$.

Step2: Simplify the \(x\)-terms using exponent rule

For the \(x\)-terms, use the exponent rule $\frac{a^m}{a^n}=a^{m - n}$. Here, \(a = x\), \(m = 7\), \(n = 5\), so $\frac{x^{7}}{x^{5}}=x^{7 - 5}=x^{2}$.

Step3: Simplify the \(y\)-terms using exponent rule

For the \(y\)-terms, use the same exponent rule. Here, \(a = y\), \(m = 7\), \(n = 6\), so $\frac{y^{7}}{y^{6}}=y^{7 - 6}=y^{1}=y$.

Step4: Combine all simplified parts

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together: $\frac{3}{5}\times x^{2}\times y=\frac{3x^{2}y}{5}$.

Answer:

$\frac{3x^{2}y}{5}$