Question

Simplify : 81 ^1/2 x 216^-2/3 x 125^1/3\64^1/6 x 243^-2/3 x3431/3

Answer 1

2161/3+641/6 Final result : 248 ——— = 82.66667 3

Step by step solution :Step  1  : 1.1     64 = 26

(64)1 = (26)1 = 26

Equation at the end of step  1  : (2161) 26 —————— + —— 3 6 Step  2  : 26 Simplify —— 6 Raising to a Power :

 2.1    26   divided by   21   = 2(6 - 1) = 25

Equation at the end of step  2  : (2161) 32 —————— + —— 3 3 Step  3  : 3.1     216 = 23•33

(216)1 = (23•33)1 = 23 • 33

Equation at the end of step  3  : (23•33) 32 ——————— + —— 3 3 Step  4  : (23•33) Simplify ——————— 3 Dividing exponents :

 4.1    33   divided by   31   = 3(3 - 1) = 32

Equation at the end of step  4  : 32 72 + —— 3 Step  5  :Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a fraction to a whole 

Rewrite the whole as a fraction using  3  as the denominator :

72 72 • 3 72 = —— = —————— 1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

72 • 3 + 32 248 ——————————— = ——— 3 3 Final result : 248 ——— = 82.66667 3