Right hand side:
(1/sqrt(23))^3
Rationalize the denominator. 1/sqrt(23) = 1/sqrt(23)×(sqrt(23))/(sqrt(23)) = (sqrt(23))/(23):
(sqrt(23))/(23)^3
Multiply each exponent in (sqrt(23))/(23) by 3:
(23^(3/2))/(23^3)
Combine powers. (23^(3/2))/(23^3) = 23^(3/2-3):
23^3/2-3
Put 3/2-3 over the common denominator 2. 3/2-3 = 3/2+(2 (-3))/2:
23^3/2-(3×2)/2
2 (-3) = -6:
23^(-6/2+3/2)
3/2-(6)/2 = (3-6)/2:
23^(3-6)/2
3-6 = -3:
23^(-3/2)
23^(-3/2) = 23^(1/2-(4)/2) = 23^(-4/2)×sqrt(23):
23^(-4/2) sqrt(23)
4/2 = (2 (-2))/2 = 2:
23^(-2) sqrt(23)
Answer:(sqrt(23))/(529)
Left hand side:
Simplify the following:
1/(23 sqrt(23))
Rationalize the denominator. 1/(23 sqrt(23)) = 1/(23 sqrt(23))×(sqrt(23))/(sqrt(23)) = (sqrt(23))/(23×23):
(sqrt(23))/(23×23)
23×23 = 529:
Answer: | (sqrt(23))/(529)
