Solve each equation. See Examples 4–6. ∜(x-15)=2

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots, which are denoted by the radical symbol (√). In the given equation, ∜(x-15) represents the fourth root of (x-15). Understanding how to manipulate and simplify these expressions is crucial for solving equations that involve them.

Isolating the Variable

Isolating the variable is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and the constants on the other. In the context of the given equation, you would first eliminate the radical by raising both sides to the fourth power, allowing you to isolate x.

Exponents and Their Properties

Exponents represent repeated multiplication and have specific properties that govern their manipulation. For instance, raising a number to a power and then taking the root can be expressed as an exponent operation. In this case, understanding how to apply the property of exponents when raising both sides of the equation to the fourth power is essential for finding the solution.