8. simplify $\frac{45x^{15}}{9x^{10}}$. (example 7)

Explanation:

Step1: Divide the coefficients

Divide 45 by 9: $\frac{45}{9}=5$.

Step2: Use exponent - subtraction rule

For the variable part with the same base $x$, use the rule $\frac{x^m}{x^n}=x^{m - n}$. Here $m = 15$ and $n = 10$, so $\frac{x^{15}}{x^{10}}=x^{15 - 10}=x^5$.

Step3: Combine the results

Multiply the result of the coefficient - division and the variable - part result: $5\times x^5 = 5x^5$.

Answer:

$5x^5$