Even Powers
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 31 of 43.
An even power hides the sign of its base: 2^4 and (-2)^4 are both 16. So x^4 = 16 has two real answers, x = 2 and x = -2. The fourth root of 16 is 2, and the negative answer comes back from the sign the power hid.
This is the same idea as x^2 = 49 giving 7 and -7, carried to higher even powers. Forgetting the negative answer is the usual mistake, so always ask first whether the power is even. If the power is not alone, get it alone before taking the root: 3x^4 = 48 becomes x^4 = 16.
An even power of a real number is never negative, so x^4 = -16 has no real answer at all.
Challenge
Solve 2x^4 - 162 = 0. Get the power alone, then find every real answer.
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