Exponent Rules Still Work

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 23 of 43.

The rules you learned for whole-number exponents hold for fractions too, as long as the base is positive. Multiplying powers of the same base adds the exponents: x^(1/3) × x^(2/3) = x^(1/3 + 2/3) = x^1, which is just x.

This agrees with what the powers mean. x^(1/3) is the cube root of x, so three of them multiplied should give x back: x^(1/3) × x^(1/3) × x^(1/3) = x^(3/3), which is x. In the same way √(x) × √(x) = x^(1/2 + 1/2), which is x.

The other rules carry over the same way. Dividing subtracts exponents, x^(5/4)/x^(1/4) = x^(4/4), and a power of a power multiplies them, (x^(1/3))^9 = x^3. Add or subtract the fractions over a common denominator, then simplify: an exponent of 4/4 is 1.

Challenge

Simplify x^(1/2) × x^(3/2). Type each line in the box under the problem and press Enter: first a single power with the exponents added, then its simplest form.

Try it yourself

x^(1/2) * x^(3/2)

Simplify the expression