Question

simplify.
\\(\frac{5x^6}{30x^4}\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients $\frac{5}{30}$. We know that 5 and 30 have a greatest common divisor of 5. So, $\frac{5}{30}=\frac{5\div5}{30\div5}=\frac{1}{6}$.

Step2: Simplify the variable part

For the variable part $x^6$ and $x^4$, we use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$ (where $m = 6$ and $n=4$). So, $\frac{x^6}{x^4}=x^{6 - 4}=x^2$.

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part. So, $\frac{5x^6}{30x^4}=\frac{1}{6}\times x^2=\frac{x^2}{6}$.

Answer:

$\frac{x^2}{6}$