The value of $\frac{[(5.4)^3-0.064]}{[(5.4)^2+2.16+0.16]}$ is _________.

5

a³ - b³ = ( a - b ) ( a² + b² + ab )

( a - b ) = \(\frac{a^3 - b^3}{a^2 + b^2 + ab }\)

$\frac{[(5.4)^3-0.064]}{[(5.4)^2+2.16+0.16]}$ this can be written as =

$\frac{[(5.4)^3-(0.4)^3]}{[(5.4)^2+2.16+(0.4)^2]}$

By comparing the above equation with the given formula we can conclude that,

a = 5.4

and b = 0.4

So the value of $\frac{[(5.4)^3-(0.4)^3]}{[(5.4)^2+2.16+(0.4)^2]}$ = 5.4 - 0.4 = 5