Question

1. \\(\frac{3a^{10}b^{6}}{6b^{2}c}\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients $\frac{3}{6}$.
$\frac{3}{6} = \frac{1}{2}$

Step2: Simplify the variable \(a\)

The variable \(a\) only appears in the numerator with exponent \(10\), so it remains \(a^{10}\).

Step3: Simplify the variable \(b\)

Use the rule of exponents for division: \( \frac{b^m}{b^n} = b^{m - n} \). Here, \(m = 6\) and \(n = 2\), so \( \frac{b^6}{b^2}=b^{6 - 2}=b^4 \).

Step4: Simplify the variable \(c\)

The variable \(c\) only appears in the denominator, so it remains in the denominator as \(c\).

Step5: Combine all parts

Multiply the simplified coefficient, \(a\) term, \(b\) term, and consider the \(c\) term. We get $\frac{1}{2} \times a^{10} \times b^4 \times \frac{1}{c}=\frac{a^{10}b^4}{2c}$

Answer:

$\frac{a^{10}b^4}{2c}$