Question

(\frac{10x}{35x^{6}})

Explanation:

Assuming the problem is to simplify the rational expression \(\frac{10x}{35x^{6}}\), here's the step - by - step solution:

Step 1: Simplify the coefficients

First, find the greatest common divisor (GCD) of 10 and 35. The factors of 10 are 1, 2, 5, 10 and the factors of 35 are 1, 5, 7, 35. The GCD of 10 and 35 is 5.
Divide both the numerator and the denominator by 5:
\(\frac{10x\div5}{35x^{6}\div5}=\frac{2x}{7x^{6}}\)

Step 2: Simplify the variable terms

When dividing variables with exponents, we use the rule \(a^{m}\div a^{n}=a^{m - n}\) (where \(a
eq0\) and \(m\geq n\)). For the variable \(x\), we have \(x^{1}\div x^{6}=x^{1 - 6}=x^{- 5}=\frac{1}{x^{5}}\) (using the rule \(a^{-n}=\frac{1}{a^{n}}\)).
So, \(\frac{2x}{7x^{6}}=\frac{2}{7}\times\frac{x}{x^{6}}=\frac{2}{7x^{5}}\)

Answer:

\(\frac{2}{7x^{5}}\)