Solve each equation. See Example 7. x^3/2 = 125

Key Concepts

Exponents and Radicals

Understanding exponents is crucial in algebra, as they represent repeated multiplication. The expression x^(3/2) indicates that x is raised to the power of 3 and then the square root is taken. This concept also involves manipulating radicals, which are expressions that include roots, such as square roots or cube roots.

Solving Exponential Equations

To solve an equation like x^(3/2) = 125, one must isolate the variable. This often involves raising both sides of the equation to the reciprocal of the exponent, in this case, 2/3, to eliminate the exponent and solve for x. This process is essential for finding the value of x that satisfies the equation.

Understanding Cube Roots

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this context, recognizing that 125 is a perfect cube (5^3) helps in simplifying the equation. Understanding cube roots is vital for solving equations involving fractional exponents, as it allows for easier manipulation of the terms.