Question

simplify the expression \\(\frac{3(a)^5}{6a^7}\\)

Explanation:

Step1: Simplify the coefficient

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

Step2: Simplify the variable part

For the variable part with the same base \(a\), we use the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\). Here, \(m = 5\) and \(n=7\), so \(\frac{a^{5}}{a^{7}}=a^{5 - 7}=a^{-2}=\frac{1}{a^{2}}\) (using the rule \(a^{-n}=\frac{1}{a^{n}}\)).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part. So we have \(\frac{1}{2}\times\frac{1}{a^{2}}=\frac{1}{2a^{2}}\).

Answer:

\(\frac{1}{2a^{2}}\)