Solve each equation. See Example 7. x^5/4 = 32

Key Concepts

Exponents and Roots

Exponents represent repeated multiplication of a base number. In the equation x^(5/4) = 32, the exponent 5/4 indicates that x is raised to the power of 5 and then the fourth root is taken. Understanding how to manipulate exponents and convert between exponential and radical forms is essential for solving such equations.

Isolating the Variable

Isolating the variable involves rearranging the equation to solve for the unknown variable, in this case, x. This often requires performing inverse operations, such as taking roots or raising to a power, to eliminate the exponent. Mastery of this technique is crucial for effectively solving equations.

Equivalence of Exponential Forms

The equivalence of exponential forms allows us to express numbers in different bases or exponents. For example, recognizing that 32 can be expressed as 2^5 helps in simplifying the equation. Understanding how to convert between different forms of numbers is vital for solving equations involving exponents.