Compute each of the following quantities 10012 14412 6413 64

Compute each of the following quantities. 100^1/2 144^1/2 64^1/3 64^4/3 5^2/5 (-8)^2/3 25^-1/2 27^-2/3

Solution

a. 100^1/2 = [(10)²]^1/2 = (10)^2*1/2 = 10¹ = 10.

b. 144^1/2 = (12²)^1/2 = (12)^2*1/2 = 12¹ = 12.

c. 64^1/2 = (8²)^1/2 = 8^2*1/2 = 8¹ = 8

d. 64^4/3 = (4³)^4/3 = 4^3*4/3 = 4⁴ = 256.

e. 5^2/5 = (5²)^1/5 = 25^1/5.

f. (-8)^2/3 = [(-2)³]^1/3 = (-2)^3*1/3 = -2.

g. 25^-1/2 = 1/25^1/2 = 1/(5²)^1/2 = 1/5^2*1/2 = 1/5

h.27^-2/3 = (3³)^-2/3 = 3^3*(-2/3) = 3^-2 = 1/3² = 1/9