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3 Tutorials that teach Applying the Properties of Exponents
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Applying the Properties of Exponents

Applying the Properties of Exponents

Description:

This lesson applies several properties of exponents to simplify expressions.

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Tutorial

  • Properties of Exponents
  • Cautions when Applying the Properties
  • Applying the Properties of Exponents

 

Properties of Exponents

There are several properties of exponents involving multiplication, division, and powers that can help us simplify expressions containing exponents.  They are:

The Product Power: a to the power of n • a to the power of m equals a to the power of n plus m end exponent

The Quotient Power: a to the power of n over a to the power of m a equals a to the power of n minus m end exponent

The Power of Powers: left parenthesis a to the power of n right parenthesis to the power of m equals a to the power of n m end exponent

Power of a Product: left parenthesis a b right parenthesis to the power of n equals a to the power of n • b to the power of n

Power of a Quotient: left parenthesis a over b right parenthesis to the power of n equals a to the power of n over b to the power of n

Negative Exponents: a to the power of negative n end exponent equals 1 over a to the power of n

 

Cautions with Applying these Properties

There are a couple of things to watch out for when applying these properties.  First, it is important to remember that the product and quotient powers can only be applied with the bases are the same. We cannot simply add the exponents if the bases are not the same. 

a to the power of n • b to the power of m not equal to left parenthesis a b right parenthesis to the power of n plus m end exponent
Secondly, the product and quotient of power properties only work with multiplication and division; they do not work with addition or subtraction. 

left parenthesis a plus b right parenthesis to the power of n not equal to a to the power of n plus b to the power of n

Applying the Properties of Exponents

Let's go through some examples where we can use different properties of exponents to simplify expressions:

EXAMPLE 1


If we see factors that appear in both the numerator and denominator, we cancel them out.  This means that we reduce the power in both the numerator and denominator. If we cancel all factors in the denominator, the denominator is 1, and doesn't need to be written. 

EXAMPLE 2