How to Multiply Exponents & Powers

An exponent is a shorter way to write a number being multiplied by itself a certain number of times. For example, an exponent could be used to simplify the expression r * r * r * r * r * r to r^6. In the term r^6, "r" is the base and "6" is the exponent. Another name for an exponent is power, such as r to the sixth power. If the exponent is two, the base is said to be "squared" and if the exponent is three the base is said to be "cubed."

Things You'll Need

• Calculator

Instructions

1. Simply any exponents that do not include variables. For example, if you had x^3 * 4^2 * x^6, you could simplify 4^2 to equal 16 so your expression would be 16 * x^3 * x^6.

2. Determine if any remaining exponents share a common base. If they do, go on to step three. If they do not, you cannot simplify the expression. For example, x^4 * x^9 have a common base: x. If you had x^6 * z^6 you cannot simplify the expression.

3. Add the exponents of numbers with common bases. For example, if you have x^4 * x^9 you would add 9 and 4 because x is the common base and the expression would simply to x^14.

4. Repeat step three for any terms that have common bases. If you had x^3 * y*7 * x^2 * z^4 * y^5, you would combine x^3 and x^2 to get x^5 and y^7 and y^5 to get y^12 so your final expression would be x^5 * y^7 * z^4.

Tips & Warnings

• Any exponent raised to the zeroth power is one. For example, f^0 equals one.

References

• It's the Law - the Law of Exponents
• Exponents: Basic Rules