Odd Powers
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 30 of 43.
To undo a power, take the matching root of both sides. For x^3 = -125, take the cube root: x is cbrt(-125), which is -5. Check: (-5)^3 = -125.
An odd power keeps the sign of its base. A positive number cubed is positive and a negative one cubed is negative, so every real number is the cube of exactly one real number, and x^3 = -125 has one real answer. The same holds for any odd power: x^5 = 32 has only the real answer x = 2, since (-2)^5 is -32.
Taking an odd root never brings in a false answer, for the same reason cubing does not: an odd power keeps signs. So there is nothing to check.
Challenge
Solve x^3 = -64. There are no move chips here: write each line yourself in the box under the equation, first x as a cube root, then its value. Negative answers are allowed.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Radicals & Rational Exponents
1Simplifying Radicals
Roots and PowersPerfect Square FactorsThe Largest SquareLetters Under the RootCube RootsRecap: Simplifying Radicals7Powers and Roots Equations
Odd PowersEven PowersFractional PowersTwo Thirds PowerRecap: Power Equations