Properties of Exponents

Exponents share a handful of properties regarding bases and their powers. Learn about each property and put it to the test in this interactive tutorial.

(For each of these concepts, see the tutorial for examples.)

Product of two powers — Assuming “x” is a real number, multiply two values with the same base by adding the exponents.

Power of a power — Assuming “x” is a real number, the exponent of an exponent is the same as raising the base to the product of the two exponents.

Power of a product — Assuming “x” and “y” are real numbers, raising the product of two values to a power is the same as raising each value to that power and multiplying the result.

(For each of these concepts, see the tutorial for examples.)

Power of a quotient — Assuming “x” and “y” are real numbers, raising the quotient of two values to a power is the same as raising each value to that power and dividing the result.

Quotient of two powers –  Assume “x” is a real number and not zero. Dividing two values with the same base and two different exponents is the same as raising the base to the difference of the two exponents.

Get More Help!

Click one of these links to get more help from another Cramlet in this same chapter:

• Decimals to Fractions
• Working With Radicals
• Rational Exponents
• Radicals and Roots
• Properties of Real Numbers
• Properties of Exponents
• Multiplying and Dividing Fractions
• Fractions, Decimals, and Percents
• Adding and Subtracting Un-Like Fractions
• Adding and Subtracting Like Fractions
• About Real Numbers
• About Exponents