Question

simplify.
\frac{36uv^{3}}{32u^{4}v^{2}}

Explanation:

Step1: Simplify coefficients

Find the greatest common divisor (GCD) of 36 and 32. The GCD of 36 and 32 is 4. Divide numerator and denominator by 4: $\frac{36\div4}{32\div4}=\frac{9}{8}$.

Step2: Simplify \( u \)-terms

Use the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. For \( u \)-terms: $\frac{u}{u^4}=u^{1 - 4}=u^{-3}=\frac{1}{u^3}$.

Step3: Simplify \( v \)-terms

For \( v \)-terms: $\frac{v^3}{v^2}=v^{3 - 2}=v^{1}=v$.

Step4: Combine all simplified parts

Multiply the simplified coefficient, \( u \)-term, and \( v \)-term: $\frac{9}{8}\times\frac{1}{u^3}\times v=\frac{9v}{8u^3}$.

Answer:

$\frac{9v}{8u^3}$