Final answer:
We can solve exponential expressions by simplifying and using rules of exponents. Quadratic equations are solvable with the quadratic formula, but higher-degree polynomials may require numerical methods. Cubing exponentials involves cubing the coefficient and tripling the exponent.
Step-by-step explanation:
The original equation provided could not be discerned accurately, but based on the information used and exemplified, the process of solving exponential and quadratic equations will be addressed.
When dealing with exponential expressions like 3²ˣ⁵, we can interpret this as 9 raised to the power of some expression (x-5), and use the rules of exponents to simplify or solve the equation. Similarly, with expressions involving fractional exponents like 3¹.⁷, we can think of this as the 10th root of 3 raised to the 17th power.
For quadratic equations of the form x² + bx + c = 0, we can use the quadratic formula to solve for x. This approach is not suitable for equations that result in cubic or higher polynomial degrees, where graphing calculators or other numerical methods like the zero function may become necessary.
When cubing exponentials, we cube the numerical term and multiply the exponent of the variable by 3, as seen in expressions like (27x³)(4x²).