By Tricia Lobo
Updated Aug 30, 2022
When working through algebraic problems, you’ll often encounter equations that involve exponents nested within one another, such as ((x'a))^b. These “double exponents” can be tackled efficiently by applying standard exponent rules and careful algebraic manipulation.
Start by reducing all numeric constants to their simplest form. For example, given ((x'2))^2 + 2'2 = 3*4, you can simplify the numbers to obtain ((x'2))^2 + 4 = 12.
Apply the fundamental exponent rule ((x'a))^b = x^{a*b}. Thus, ((x'2))^2 simplifies to x^4.
Move all constant terms to the opposite side of the equation. Subtract 4 from both sides to get x^4 = 8.
Take the fourth root of each side to solve for x. The solution set is x = (8'{1/4}) or x = -(8'{1/4}).
Following these steps ensures you handle double exponents systematically and arrive at correct, reliable results.
