Question

simplify.\\(\frac{36y^2 z}{9y^3 z^5}\\)

Explanation:

Step1: Simplify coefficients

Divide the coefficient 36 by 9: $\frac{36}{9} = 4$

Step2: Simplify \( y \)-terms

Use the rule \( \frac{a^m}{a^n} = a^{m - n} \) for \( y \): $\frac{y^2}{y^3} = y^{2 - 3} = y^{-1} = \frac{1}{y}$

Step3: Simplify \( z \)-terms

Use the rule \( \frac{a^m}{a^n} = a^{m - n} \) for \( z \): $\frac{z}{z^5} = z^{1 - 5} = z^{-4} = \frac{1}{z^4}$

Step4: Combine results

Multiply the simplified coefficient, \( y \)-term, and \( z \)-term: $4 \times \frac{1}{y} \times \frac{1}{z^4} = \frac{4}{y z^4}$

Answer:

$\frac{4}{y z^4}$