Question

Evaluate:
a) 8^2/3
b)6^1/2 x 6^3/2
c)(8/27)61/3

Please explain how you solved this. Thanks for the help in advance. :)

Answer 1

a) 8^(2/3) can be written as = [8^(1/3) ]² and also (8²)^(1/3)                       Here you have to observe if 8 can be written as cue of a number. You will see that 8 can be written as 2³. Hence we write [8^(1/3)]² = [ {2³}^(1/3)]² = 2² = 4 because (2³)^(1/3) = 2^{3x(1/3)} = 2^1 = 2.                                       b) 6^(1/2) x 6^(3/2) = 6^[(1/2) + (3/2)] = 6^(2) [Because 1/2 + 3/2=4/2 = 2] = 36.
c) (8/27)^(1/3)  . Here also [as in question (a) above] find if 8 can be written as cube of a number and also if 27 can be written as cube of a number. You will see that 8 can be written as cube of 2, also 27 can be written as cube of 3.  Therefore (8/27)^(1/3)  = [8^(1/3)] / [27^(1/3)] = [{2³}^(1/3)] / [{3^3}^(1/3)] = 2^[3x(1/3)] / 3^[3X(1/3)] = (2^1) / (3^1) = 2/3

Answer 2

a)
=$8^{\frac{2}{3}}$

=$2^{3.{\frac{2}{3}}}$ 

=$2^{2}$

=$4$

b)
  
=$6^{\frac{1}{2}+\frac{3}{2}}$

=$6^{\frac{1+3}{2}}$

=$6^{2}$

=$36$

c)

=$\frac{8}{27}.\frac{61}{3}$

=$\frac{8}{27}.\frac{61}{3}$

=$6.024$