Evaluate the expression by hand.

Question

Evaluate the expression by hand. 

 

  216^5/6  

  216^1/2

Answer 1

(216)^(5/6)/(216)^(1/2)=

(216)^(5/6)-(1/2)=

(216)[^(5-3)/6=

(216)^(2/6)=

(216)^(1/3)=

6

 

Answer 2

This is mainly about the exponents.  When you divide the same number (216) with exponents you subtract the exponent in the denominator (bottom) from the numerator (top).  In this example: 5/6-1/2=1/3.

 

You really have 216^1/3.  If they are looking to have you simplify further you only need to take the cube root of 216. 

Answer 3

(216^(5/6))/(216^(1/2)) =

 

216^((5-3)/6) =

 

216^(1/3)

 

216 = 6*36 = 6*6*6 = 6^3

 

216^(1/3) = (6^3)^(1/3) = 6