Question

Find the value of :

`({0.000064})^{ (5)/(6) }`

​

Answer 1

Observe that

8² = 64

(1/1000)² = 1/1000000 = 0.00001

8² × (1/1000)² = 64 × 0.000001 = 0.000064

Then

`(0.000064)^(5/6) = \left(\left(\frac8{1000}\right)^2\right)^(5/6) \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\frac8{1000}\right)^(5/3) \\\\ ~~~~~~~~~~~~~~~~~~ = \left((2^3)/(10^3)\right)^(5/3) \\\\ ~~~~~~~~~~~~~~~~~~ = \left(\frac2{10}\right)^5 \\\\ ~~~~~~~~~~~~~~~~~~ = (2^5)/(10^5) \\\\ ~~~~~~~~~~~~~~~~~~ = (32)/(100000) = \boxed{\frac1{3125} = 0.00032}`