properties of rational exponents

By: Matthew Iommi & Noah Phillips

Rational Exponents and Radical Notation

Convert fractional exponent to a root with a power. The denominator goes in the front of the root than the numerator becomes a power.

Product of power property

To find a power of a product, find the power of each factor and then multiply. In general, (ab)^m = a^m · b^m. In other words, you can keep the exponent the same and multiply the bases


Quotient of powers property

Subtract each number's exponents if the same number is being divided ,then add the subtracted exponent to one of the original numbers.

Power of power property

If the number has two exponents then you can just multiply the two exponents to get one.

power of a product property

Distribute the exponent to each number. Then proceed with problem.

Power of a Quotient property

Distibute the exponent to each number then proceed with problem.