Question

simplify.
\\(\frac{56u^{4}v^{4}}{48u^{3}v^{4}}\\)

Explanation:

Step1: Simplify the coefficients

Find the greatest common divisor (GCD) of 56 and 48. The GCD of 56 and 48 is 8. Divide both 56 and 48 by 8: $\frac{56\div8}{48\div8} = \frac{7}{6}$.

Step2: Simplify the \(u\)-terms

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

Step3: Simplify the \(v\)-terms

Using the same exponent rule, for the \(v\)-terms: $\frac{v^4}{v^4}=v^{4 - 4}=v^0 = 1$ (since any non - zero number to the power of 0 is 1).

Step4: Multiply the simplified parts together

Multiply the simplified coefficient, \(u\)-term, and \(v\)-term: $\frac{7}{6}\times u\times1=\frac{7u}{6}$.

Answer:

$\frac{7u}{6}$