Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents. Product of Powers Property: This property states that to multiply powers having the same base, add the exponents.

Quotient of Powers Property: This property states that to divide powers having the same base, subtract the exponents. That is, for a non-zero real number a and two integers m and n. Power of a Product Property: This property states that the power of a product can be obtained by finding the powers of each factor and multiplying them. Power of a Quotient Property: This property states that the power of a quotient can be obtained by finding the powers of numerator and denominator and dividing them.

That is, for any two non-zero real numbers a and b and any integer m. In the above figure, the letter R is on the top. Related Links Denominator. Definition Of Power Properties Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.This is an example of the product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.

This is an example of the quotient of powers property and tells us that when you divide powers with the same base you just have to subtract the exponents. When you raise a quotient to a power you raise both the numerator and the denominator to the power. In earlier chapters we talked about the square root as well.

The square root of a number x is the same as x raised to the 0. In earlier chapters we introduced powers. Share on Facebook. Search Pre-Algebra All courses. All courses. Algebra 1 Discovering expressions, equations and functions Overview Expressions and variables Operations in the right order Composing expressions Composing equations and inequalities Representing functions as rules and graphs.

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Algebra 1 Exponents and exponential functions Overview Properties of exponents Scientific notation Exponential growth functions About Mathplanet. Algebra 1 Radical expressions Overview The graph of a radical function Simplify radical expressions Radical equations The Pythagorean Theorem The distance and midpoint formulas.

Algebra 1 Rational expressions Overview Simplify rational expression Multiply rational expressions Division of polynomials Add and subtract rational expressions Solving rational expressions.We know how to calculate the expression 5 x 5. This expression can be written in a shorter way using something called exponents. The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

If two powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents. If two powers have the same base then we can divide the powers. When we divide powers we subtract their exponents. The rule for the power of a power and the power of a product can be combined into the following rule:.

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## Properties of exponents

Pre-Algebra More about the four rules of arithmetic Overview Integers and rational numbers Learn how to estimate calculations Calculating with decimals and fractions Geometric sequences of numbers Scientific notation. Pre-Algebra More about equation and inequalities Overview Fundamentals in solving Equations in one or more steps Calculating the circumference of a circle. Pre-Algebra Graphing and functions Overview Linear equations in the coordinate plane The slope of a linear function Graphing linear inequalities Solve systems of equations by graphing.

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## Power of a Power Property

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### Powers and exponents

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### Exponent rules

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**Power Rule for Exponents**

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