Question

express the following fraction in simplest form using only positive exponents.\\(\frac{2s^{9}}{3(s)^{4}}\\)

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{s^m}{s^n} = s^{m - n} \) (where \( m > n \) for positive exponents here). So for \( \frac{s^9}{s^4} \), we have \( s^{9 - 4} \).
\( \frac{2s^9}{3s^4} = \frac{2}{3} \times s^{9 - 4} \)

Step2: Simplify the exponent

Calculate \( 9 - 4 = 5 \). So the expression becomes \( \frac{2}{3}s^5 \).

Answer:

\(\dfrac{2}{3}s^{5}\)