Question

simplify.\\(
\frac{40wx^{2}}{5w^{5}x^{3}}
\\)\\(
\boxed{}
\\)

Explanation:

Step1: Simplify the coefficients

Divide the coefficient of the numerator by the coefficient of the denominator. So, $\frac{40}{5} = 8$.

Step2: Simplify the \( w \)-terms

Use the rule of exponents for division: \( \frac{a^m}{a^n} = a^{m - n} \). For the \( w \)-terms, we have \( \frac{w}{w^5} = w^{1 - 5} = w^{-4} \), and by the negative exponent rule \( a^{-n}=\frac{1}{a^n} \), this becomes \( \frac{1}{w^4} \).

Step3: Simplify the \( x \)-terms

Using the same exponent rule for division, for the \( x \)-terms, \( \frac{x^2}{x^3} = x^{2 - 3} = x^{-1}=\frac{1}{x} \).

Step4: Combine the simplified terms

Multiply the simplified coefficient, \( w \)-term, and \( x \)-term together. So we have \( 8\times\frac{1}{w^4}\times\frac{1}{x}=\frac{8}{w^4x} \).

Answer:

\(\dfrac{8}{w^{4}x}\)