The value of $$\frac{(0.42)^2 + 36(0.05)^2}{9(0.21)^2 + (0.45)^2}$$​ is:

Correct option is D

Given:

​$$\frac{(0.42)^2 + 36(0.05)^2}{9(0.21)^2 + (0.45)^2}$$​​

Formula Used:

​$$(x^a)^b = x^{ab}$$​​

Solution:

​$$\frac{(0.42)^2 + 36(0.05)^2}{9(0.21)^2 + (0.45)^2}$$​​

​$$\frac{(2\times 0.21)^2 + 36(0.05)^2}{9(0.21)^2 + (9 \times 0.05)^2}$$​​

​$$\frac{4( 0.21)^2 + 36(0.05)^2}{9(0.21)^2 + 81(0.05)^2}$$​​

​$$\frac{4[( 0.21)^2 + 9(0.05)^2]}{9[(0.21)^2 + 9(0.05)^2]}$$​​

​$$= \frac{4}{9}$$​​