Question

simplify. express your answer using positive exponents. 4u^{2}cdot7u^{ - 3}

Explanation:

Step1: Apply quotient - rule of exponents

When dividing two terms with the same base \(a^m\div a^n=a^{m - n}\), for the given expression \(\frac{4u^{2}}{7u^{13}}\), the base is \(u\), \(m = 2\) and \(n=13\). Also, divide the coefficients.
\(\frac{4u^{2}}{7u^{13}}=\frac{4}{7}u^{2-13}\)

Step2: Simplify the exponent

Calculate \(2 - 13=- 11\), so we have \(\frac{4}{7}u^{-11}\).

Step3: Rewrite with positive exponent

Using the rule \(a^{-n}=\frac{1}{a^{n}}\), we rewrite \(\frac{4}{7}u^{-11}\) as \(\frac{4}{7u^{11}}\)

Answer:

\(\frac{4}{7u^{11}}\)