Negative Exponents
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 22 of 43.
A negative exponent means one over, just as it did with whole numbers: 5^(-2) = 1/5^2 = 1/25. The minus in the exponent does not flip the sign of the answer. It moves the power below the line. One over a fraction turns it upside down, so a fraction base flips: (2/5)^(-2) = (5/2)^2 = 25/4.
With a fraction exponent, deal with the minus first, then the fraction as in the last lesson. Take 25^(-3/2):
25^(-3/2) = 1/25^(3/2) = 1/(25^(1/2))^3 = 1/5^3 = 1/125
Why one over? Multiply 25^(3/2) by 25^(-3/2) and the exponents add to 0, and 25^0 = 1. Two numbers whose product is 1 are each other's reciprocals, so 25^(-3/2) must be one over 25^(3/2).
Challenge
Work out 8^(-2/3). Type each line in the box under the problem and press Enter: move the power below the line, write its root and power as two steps, then finish the value.
Try it yourself
Simplify the expression
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 Equations5Rational Exponents
One Over nm Over nNegative ExponentsExponent Rules Still WorkRecap: Rational Exponents