Question

(\frac{18a^{4}bc^{10}}{39ab^{5}c^{3}})

Explanation:

Step1: Simplify coefficients

Find the greatest common divisor (GCD) of 18 and 39. The GCD of 18 and 39 is 3. Divide numerator and denominator by 3: $\frac{18\div3}{39\div3}=\frac{6}{13}$.

Step2: Simplify variable \(a\)

Use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$. For \(a\): $\frac{a^4}{a^1}=a^{4 - 1}=a^3$.

Step3: Simplify variable \(b\)

For \(b\): $\frac{b^1}{b^5}=b^{1 - 5}=b^{-4}=\frac{1}{b^4}$ (using $\frac{x^m}{x^n}=x^{m - n}$).

Step4: Simplify variable \(c\)

For \(c\): $\frac{c^{10}}{c^3}=c^{10 - 3}=c^7$ (using $\frac{x^m}{x^n}=x^{m - n}$).

Step5: Combine all simplified parts

Multiply the simplified coefficient, \(a\), \(b\), and \(c\) parts together: $\frac{6}{13}\times a^3\times\frac{1}{b^4}\times c^7=\frac{6a^3c^7}{13b^4}$.

Answer:

$\frac{6a^3c^7}{13b^4}$