Question

find the value of 1 by 216 to the power 2 by 3 + 1 by 256 to the power 3 by 4 + 1 by 243 to the power minus 1 by 5​

Answer 1

Step-by-step explanation:

Given :-

(1/216)⅔ + (1/256)¾ + (1/243)⅕

To find :-

Find the value of the expression ?

Solution :-

Given expression is

(1/216)⅔ + (1/256)¾ + (1/243)⅕

216 = 6×6×6 = 6³

216 can be written as 6³

256 = 4×4×4×4 = 4³

256 can be written as 4⁴

243 = 3×3×3×3×3 = 3⁵

243 can be written as 3⁵

Now,

The given expression becomes

=> (1/6³)⅔ + (1/4⁴)¾ + (1/3⁵)⅕

=> [(1/6)³]⅔ + [(1/4)⁴]¾ + [(1/3)⁵]⅕

=> [(1/6)³×⅔]+ [(1/4)⁴×¾] + [(1/3)⁵×⅕]

Since, (a^m)^n = a^(mn)

=> (1/6)² + (1/4)³ + (1/3)¹

=> (1/36) + (1/64) + (1/3)

LCM of 36 , 64 and 3 = 576

=> [(1×16)+(1×9)+(1×192)]/576

=> (16+9+192)/576

=> 217/576

Answer:-

The value of the given expression is 217/576

Used formulae:-

→ (a^m)^n = a^(mn)

→ (a/b)^m = a^m / b^m