Question

simplify.
\\(\frac{40y^{4}z}{8y^{5}z^{4}}\\)

Explanation:

Step1: Simplify the coefficients

Divide the coefficient 40 by 8: $\frac{40}{8} = 5$

Step2: Simplify the \( y \)-terms

Using the rule of exponents \( \frac{a^m}{a^n} = a^{m - n} \), for \( y \)-terms: \( \frac{y^4}{y^5} = y^{4 - 5} = y^{-1} = \frac{1}{y} \)

Step3: Simplify the \( z \)-terms

Using the rule of exponents \( \frac{a^m}{a^n} = a^{m - n} \), for \( z \)-terms: \( \frac{z}{z^4} = z^{1 - 4} = z^{-3} = \frac{1}{z^3} \)

Step4: Combine the results

Multiply the simplified coefficient, \( y \)-term, and \( z \)-term: \( 5\times\frac{1}{y}\times\frac{1}{z^3} = \frac{5}{y z^3} \)

Answer:

\( \frac{5}{y z^3} \)