The value of $\frac{0.49-0.7\times 0.8+0.64}{0.512+0.343}$ is:

Let's represent the decimals using variables to recognize standard algebraic forms:Let $a=0.7$ and $b=0.8$.Then, $0.49=(0.7{)}^2=a^2$$0.64=(0.8{)}^2=b^2$$0.512=(0.8{)}^3=b^3$$0.343=(0.7{)}^3=a^3$ The given expression can be written as:
$$\frac{a^2-ab+b^2}{b^3+a^3}$$
Using the identity for the sum of two cubes ($a^3+b^3=(a+b)(a^2-ab+b^2)$):
$$\frac{a^2-ab+b^2}{(a+b)(a^2-ab+b^2)}=\frac{1}{a+b}$$
Substituting the values back:
$$\frac{1}{0.7+0.8}=\frac{1}{1.5}=\frac{10}{15}=\frac{2}{3}$$