Question

simplify.
\frac{9x^{5}}{45x^{3}}

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{9}{45} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 9. So, \( \frac{9\div9}{45\div9}=\frac{1}{5} \).

Step2: Simplify the variable terms

For the variable \( x \), we use the quotient rule of exponents, which states that \( \frac{x^m}{x^n}=x^{m - n} \) where \( m \) and \( n \) are real numbers and \( x
eq0 \). Here, \( m = 5 \) and \( n = 3 \), so \( \frac{x^5}{x^3}=x^{5 - 3}=x^2 \).

Step3: Combine the simplified parts

Multiply the simplified coefficient and the simplified variable term together. So, \( \frac{1}{5}\times x^2=\frac{x^2}{5} \).

Answer:

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