Question

express the following fraction in simplest form using only positive exponents.\\(\frac{4(v^{3})^{2}}{2v^{5}}\\)

Explanation:

Step1: Simplify the coefficient and use exponent rule \((a^m)^n = a^{mn}\)

First, simplify the coefficient \(\frac{4}{2}=2\). Then, for the variable part, use the power of a power rule \((v^3)^2 = v^{3\times2}=v^6\). So the expression becomes \(\frac{2v^6}{v^5}\).

Step2: Use the quotient rule for exponents \(a^m\div a^n = a^{m - n}\)

For the variable \(v\), apply the quotient rule: \(v^6\div v^5 = v^{6 - 5}=v^1 = v\). Multiply by the coefficient 2, we get \(2v\).

Answer:

\(2v\)