Question

Simplify(64/125)∧-2/3  +1/(256/625)∧1/4  +√253/ 3√64

Answer 1

Given, (64/125)^-2/3  +1/(256/625)^1/4  +root 253/ 3 root 64

Which can be written as,

 = (125/64)^2/3  + (625/256)^1/4  +root 253/ 3 * 8 

 = (5^3/4^3)^2/3  + (5^4/4^4)^1/4 + root 253/8

 = 25/16 + 5 + root 253/4

 = 25 + 4(5+root 253)/16

 = 25+20+4root253/16

 = 45+4root253/16

Hope this helps!

Answer 2

(64/125)^-2/3 +1/(256/625)^1/4 + √253/ 3√64

◾We can also write it as,

➡ (125/64)^2/3 + (625/256)^1/4 + √253/ 3 * 8

➡ (5^3/4^3)^2/3 + (5^4/4^4)^1/4 + √253/8

➡ 25/16 + 5 + √253/4

➡ 25 + 4(5+ √253)/16

➡ 25+20+4√253/16

➡ 45+4√253/16