Question

Tính:

a) \(\dfrac{5^4.20^4}{25^3.4^5}\)

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

Answer 1

a) `(5^4 . 20^4)/(25^3 .4^5)`

`=(5^4 . (5.4)^4)/((5^2)^3 .4^5)`

`= (5^4 . 5^4 . 4^4)/(5^6 . 4^5)`

`= (5^2)/4=25/4`

b) `(-10/3)^5 . (-6/5)^4`

`=-10/3 . [(-10/3) . (-6/5)]^4`

`= -10/3 . [ (-5.2 . (-2).3)/(3.5)]^4`

`=-10/3 . 4^4`

`=-2560/3`

Answer 2

A) \(=\dfrac{\left(5.20\right)^4}{\left(25.4\right)^5}=\dfrac{100^4}{100^5}=\dfrac{1}{100}\)

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

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

   =\(\left(\dfrac{-10}{3}\right).\left(\dfrac{60}{15}\right)^4\)

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

   =\(\left(\dfrac{-10}{3}\right).256\)

   =\(\dfrac{-2650}{3}\)

 

Answer 3

a) \(\dfrac{5^4.20^4}{25^3.4^5}=\dfrac{5^4.4^4.5^4}{5^6.4^5}=\dfrac{5^2}{4}=\dfrac{25}{4}\) 

b) \(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4=\left(\dfrac{-10}{3}\right)^4.\left(\dfrac{-10}{3}\right).\left(\dfrac{-6}{5}\right)^4=\left(\dfrac{-10}{3}.\dfrac{-6}{5}\right)^4.\left(\dfrac{-10}{3}\right)=\left(4\right)^4.\left(\dfrac{-10}{3}\right)=256.\left(\dfrac{-10}{3}\right)=\dfrac{-2560}{3}\)