Question

(-10/3)⁵.(-6/5)⁴

Answer 1

\(\left(-\dfrac{10}{3}\right)^5.\left(-\dfrac{6}{5}\right)^4\\ =\left(-\dfrac{10}{3}\right)^5.\left(\dfrac{6}{5}\right)^4\\ =-\left(\dfrac{10}{3}\right)^5.\left(\dfrac{6}{5}\right)^4\\ =-\dfrac{10^5.6^4}{3^5.5^4}=-\dfrac{2^5.5^5.3^4.2^4}{3^5.5^4}\\ =-\dfrac{2^9.3^4.5^4.5}{3.3^4.5^4}\\ =-\dfrac{2^9.5}{3}=-\dfrac{2560}{3}\)

Answer 2

\(=\dfrac{-100000}{243}\times\dfrac{1296}{625}=\dfrac{\left(-100000\right).1296}{243.625}=\dfrac{\left(-160\right).625.1296}{625.243}=\dfrac{-160.1296}{243}=\dfrac{81.16.\left(-160\right)}{81.3}=\dfrac{16.\left(-160\right)}{3}=\dfrac{-2560}{3}\)

Answer 3

\(\left(\dfrac{-10}{3}\right)^5\times\left(\dfrac{-6}{5}\right)^4\)

\(=\left(-\dfrac{10}{3}\right)\times\left(-\dfrac{10}{3}\right)^4\times\left(-\dfrac{6}{5}\right)^4\)

\(=\left(-\dfrac{10}{3}\right)\times\left(-\dfrac{10}{3}\times-\dfrac{6}{5}\right)^4\)

\(=\left(-\dfrac{10}{3}\right)\times\left(60\times15\right)^4\)

\(=4^4\times\left(-\dfrac{10}{3}\right)\)

\(=-\dfrac{2560}{3}\)