Question

simplify. express your answer using positive exponents. $\frac{7r^{8}s^{5}t}{r^{6}s^{8}t^{9}}$

Explanation:

Step1: Apply exponent - division rule for r

When dividing terms with the same base \(a^m\div a^n=a^{m - n}\), for \(r\) we have \(r^8\div r^6=r^{8 - 6}=r^2\).

Step2: Apply exponent - division rule for s

For \(s\), \(s^5\div s^8=s^{5 - 8}=s^{- 3}=\frac{1}{s^{3}}\) (to get positive exponent).

Step3: Apply exponent - division rule for t

For \(t\), \(t\div t^9=t^{1-9}=t^{-8}=\frac{1}{t^{8}}\) (to get positive exponent).

Step4: Combine the results

The original expression \(\frac{7r^8s^5t}{r^6s^8t^9}=7\times r^2\times\frac{1}{s^{3}}\times\frac{1}{t^{8}}=\frac{7r^2}{s^{3}t^{8}}\)

Answer:

\(\frac{7r^2}{s^{3}t^{8}}\)