m Over n
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 21 of 43.
A power like 25^(3/2) has two jobs. Split the exponent: 3/2 is 1/2 times 3, so by the power of a power rule 25^(3/2) = (25^(1/2))^3. The bottom of the fraction says which root to take, and the top says which power to raise it to.
25^(3/2) = (25^(1/2))^3 = 5^3 = 125
In general, for a not negative, a^(m/n) = (a^(1/n))^m: the nth root first, then the power m. You could do the power first, 25^3 = 15625, and then take the square root of 15625. That gives 125 too, since both orders reach the same exponent. But the root first keeps the numbers small enough to do in your head.
Challenge
Work out 16^(3/4). Type each line in the box under the problem and press Enter: first the root and the power as two steps, then each simpler line until one number is left.
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