$$\left(a+b\right)^2=\left(a+b\right)\ \left(a+b\right)$$
$$=a^2+ab+ab+b^2$$
$$=a^2+b^2+2ab$$
$$AND\ $$
$$\left(a-b\right)^2=\left(a-b\right)\ \left(a-b\right)$$
$$=a^2-ab-ab+b^2$$
$$=a^2+b^2-2ab$$
$$\frac{3^{\left(a+b\right)^2}}{3^{\left(a-b\right)^2}}$$
$$=\frac{3^{a^2+b^2+2ab}}{3^{a^2+b^2-2ab}}$$
$$u\sin g\ division\ law\ of\ indices=>\ \frac{x^y}{x^z}=x^{y-z}$$
$$=>3^{\left(a^2+b^2+2ab\right)-\left(a^2+b^2-2ab\right)}$$
$$=>3^{\left(2ab+2ab\right)}$$
$$=>3^{\left(4ab\right)}$$
Statement 1 => a + b = 7
$$Therefore,\ numerator\ =\ 3^{\left(7\right)^2}=3^{49}$$
But denominator cannot be estimated because a - b is unknown. Hence, the given expression cannot be evaluated and the target question cannot be answered.
Statement 1 is NOT SUFFICIENT
Statement 2 => ab=12
$$From\ the\ question\ stem\ =>3^{4ab}$$
$$where\ ab\ =\ 12$$
$$=>3^{4\cdot12}=3^{48}$$
Statement 2 alone is SUFFICIENT
Answer = B
