The value of $$\frac{{0.3}^4-{0.2}^4}{{0.3}^2+{0.2}^2}$$​ is:

Correct option is A

Given:

$$\frac{0.3^4 - 0.2^4}{0.3^2 + 0.2^2}$$​

Formula Used:

​$$a^4 - b^4 = (a^2 - b^2)(a^2 + b^2)$$​

​Solution:​

$$\frac{(0.3^2 - 0.2^2)(0.3^2 + 0.2^2)}{0.3^2 + 0.2^2}$$​

= 0.09 - 0.04 = 0.05

Thus, the value of the expression is 0.05.

Alternate Method:

$$\frac{0.3^4 - 0.2^4}{0.3^2 + 0.2^2}$$​​

​$$=\frac{0.0081 - 0.0016}{0.09 + 0.04}$$​

$$=\frac{0.0065}{0.13} = 0.05$$​