Solve 49^10a-b^12x/81

$${ 49 }^{ 10a } - \frac{ { b }^{ 12x } }{ 81 }$$

Factor

$$\frac{\left(3\times \left(7^{a}\right)^{5}-\left(b^{x}\right)^{3}\right)\left(\left(b^{x}\right)^{3}+3\times \left(7^{a}\right)^{5}\right)\left(\left(b^{x}\right)^{6}+9\times \left(7^{a}\right)^{10}\right)}{81}$$

Solution Steps

Factor out \frac{1}{81}.

$$\frac{81\times 49^{10a}-b^{12x}}{81}$$

Consider 81\times \left(49^{a}\right)^{10}-\left(b^{x}\right)^{12}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(9\times \left(49^{a}\right)^{5}-\left(b^{x}\right)^{6}\right)\left(9\times \left(49^{a}\right)^{5}+\left(b^{x}\right)^{6}\right)$$

Rewrite the complete factored expression.

$$\frac{\left(9\times \left(49^{a}\right)^{5}-\left(b^{x}\right)^{6}\right)\left(9\times \left(49^{a}\right)^{5}+\left(b^{x}\right)^{6}\right)}{81}$$

Evaluate

$$-\frac{b^{12x}}{81}+7^{20a}$$