Variables
Description
What is this formula?
This formula calculates the value of x from an equation of the form:
y = a·xⁿ
It isolates the variable x by dividing the result by the coefficient and then applying the inverse power operation. This is one of the standard techniques for solving explicit power equations.
When to use it
Use this formula when the unknown variable is raised to a known power and all other quantities are known. It is commonly used to solve polynomial equations, engineering formulas, physical models, and geometric relationships.
Example
Given:
y = 49
a = 7
n = 2
Formula:
x = (y/a)^(1/n)
Substitution:
x = (49/7)^(1/2)
Result:
x ≈ 2.646
The calculated value of x satisfies the original equation.
Applications
Algebra
Engineering calculations
Geometry
Physics
Scientific analysis
Note
This formula is valid when the coefficient a is nonzero and the exponent n is known. For even values of n, the radicand must be nonnegative to obtain real-valued solutions. Depending on the application, negative roots may also satisfy the original equation.