Question

simplify.
\\(\frac{45uv^5}{18u^2v^2}\\)

Explanation:

Step1: Simplify numerical coefficients

Find the greatest common divisor of 45 and 18, which is 9. Divide both by 9:
$\frac{45}{18} = \frac{5}{2}$

Step2: Simplify $u$ terms

Use exponent rule $\frac{u^a}{u^b}=u^{a-b}$:
$\frac{u^1}{u^2} = u^{1-2}=u^{-1}=\frac{1}{u}$

Step3: Simplify $v$ terms

Use exponent rule $\frac{v^a}{v^b}=v^{a-b}$:
$\frac{v^5}{v^2} = v^{5-2}=v^3$

Step4: Combine all simplified parts

Multiply the results from Steps 1-3:
$\frac{5}{2} \times \frac{1}{u} \times v^3$

Answer:

$\frac{5v^3}{2u}$