Question

(\frac{4(u^{5})^{3}}{20u^{10}})

Explanation:

Step1: Simplify the numerator's exponent

Using the power of a power rule \((a^m)^n = a^{m\times n}\), for \((u^5)^3\), we get \(u^{5\times3}=u^{15}\). So the numerator becomes \(4u^{15}\).

Step2: Simplify the fraction's coefficient

Simplify \(\frac{4}{20}\) by dividing numerator and denominator by their greatest common divisor, which is 4. So \(\frac{4}{20}=\frac{1}{5}\).

Step3: Simplify the variable's exponent

Using the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\), for \(\frac{u^{15}}{u^{10}}\), we get \(u^{15-10}=u^5\).

Step4: Combine the results

Multiply the simplified coefficient and the simplified variable term: \(\frac{1}{5}\times u^5=\frac{u^5}{5}\).

Answer:

\(\frac{u^5}{5}\)