Simplify 24t^315t^4 5t^83t^6.

24t^315t^4 5t^83t^6 =2415 t^3t^4 53 t^8t^6 = 85 1t 53 t^2 = (85 53) (1t t^2) = 83 t = 8t3.

jmc

algebra intermediate

Problem

Simplify

\frac{24 t ^{3}}{15 t ^{4}} \cdot \frac{5 t ^{8}}{3 t ^{6}}

Solution

\frac{24 t ^{3}}{15 t ^{4}} \cdot \frac{5 t ^{8}}{3 t ^{6}} = \frac{24}{15} \cdot \frac{t ^{3}}{t ^{4}} \cdot \frac{5}{3} \cdot \frac{t ^{8}}{t ^{6}} = \frac{8}{5} \cdot \frac{1}{t} \cdot \frac{5}{3} \cdot t^{2} = (\frac{8}{5} \cdot \frac{5}{3}) \cdot (\frac{1}{t} \cdot t^{2}) = \frac{8}{3} \cdot t = \frac{8 t}{3}

Final answer

\frac{8t}{3}