\(\frac{24t^3}{15t^4}*\frac{5t^8}{3t^6}\)
Simplify \(\frac{24t^3}{15t^4}\)
Both 24 and 15 have a common factor of 3
\(\frac{24t^3}{15t^4} = \frac{8t^3}{5t^4}\)
\(\frac{8t^3}{5t^4}*\frac{5t^8}{3t^6}\)
Apply exponent rule: \(\frac{x^a}{x^b} = \) 1/x^b-a
\(\frac{8}{5t}\)
Continue
\(\frac{8}{5t}*\frac{5t^8}{3t^6}\)
Apply exponent rule: \(\frac{x^a}{x^b} = \) x^a-b
\( \frac{5t^2}{3}\)
Continue
\(\frac{8}{5t} * \frac{5t^2}{3}\)
\(\frac{8*5t^2}{5t*3}\)
\(\frac{8t^2}{t*3}\)
\(\frac{8t}{3}\)
Your answer would be \(\frac{8t}{3}\)
Hope this helps ;P