a*b=a^3+3^b-ஐ தீர்க்கவும்

$$a * b = a ^ { 3 } + 3 ^ { b }$$

a-க்காகத் தீர்க்கவும்

$$\left\{\begin{matrix}a=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}\right)^{-\frac{1}{3}}\left(3\left(-\sqrt{3}i-1\right)\times \left(\frac{-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}}{9}\right)^{\frac{2}{3}}+2\times 2^{\frac{2}{3}}b\right)}{8}\text{; }a=\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}\right)^{-\frac{1}{3}}\left(3\times \left(\frac{-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}}{9}\right)^{\frac{2}{3}}+2^{\frac{2}{3}}b\right)}{2}\text{; }a=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}\right)^{-\frac{1}{3}}\left(3\left(-1+\sqrt{3}i\right)\times \left(\frac{-9\times 3^{b}+\sqrt{3\left(27\times 9^{b}-4b^{3}\right)}}{9}\right)^{\frac{2}{3}}+2\times 2^{\frac{2}{3}}b\right)}{8}\text{, }&b\neq 0\\a=-1\text{; }a=e^{\frac{\pi i}{3}}\approx 0.5+0.866025404i\text{; }a=e^{\frac{5\pi i}{3}}\approx 0.5-0.866025404i\text{, }&b=0\end{matrix}\right.$$