The value of $$\frac{(4.6)^4 + (5.4)^4 + (24.84)^2}{4.6)^2 + (5.4)^2 + 24.84}$$ is:

$$\frac{(4.6)^4 + (5.4)^4 + (24.84)^2}{(4.6)^2 + (5.4)^2 + 24.84}$$

Addition and subtraction of  (24.84)^2 in the numerator.

$$\frac{(4.6)^4 + (5.4)^4 + (24.84)^2 + (24.84)^2 - (24.84)^2}{(4.6)^2 + (5.4)^2 + 24.84}$$

$$\frac{(4.6)^4 + (5.4)^4 + 2 \times(24.84)^2  - (24.84)^2}{(4.6)^2 + (5.4)^2 + 24.84}$$

$$\frac{((4.6)^2 + (5.4)^2 )^2 - (24.84)^2}{(4.6)^2 + (5.4)^2 + 24.84}$$

($$\because (a +b)^2 = a^2 + b^2 + 2ab$$)

$$\frac{((4.6)^2 + (5.4)^2 - (24.84))((4.6)^2 + (5.4)^2 + (24.84))}{(4.6)^2 + (5.4)^2 + 24.84}$$

($$\because a^2 - b^2 = (a - b)(a+b)$$)

$$(4.6)^2 + (5.4)^2 - (24.84)$$ = 21.16 + 29.16 - 24.84 = 25.48