Combining Properties to Simplify Expressions

Learning Outcomes

  • Simplify quotients that require a combination of the properties of exponents

We’ll now summarize all the properties of exponents so they are all together to refer to as we simplify expressions using several properties. Notice that they are now defined for whole number exponents.

Summary of Exponent Properties

If a,b are real numbers and m,n are whole numbers, then

Product Propertyaman=am+nPower Property(am)n=amnProduct to a Power Property(ab)m=ambmQuotient Propertyaman=amn,a0,m>naman=1anm,a0,n>mZero Exponent Definitiona0=1,a0Quotient to a Power Property(ab)m=ambm,b0

 

example

Simplify: (x2)3x5.

Solution

(x2)3x5
Multiply the exponents in the numerator, using the

Power Property.

x6x5
Subtract the exponents. x

 

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example

Simplify: m8(m2)4

 

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example

Simplify: (x7x3)2

 

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example

Simplify: (p2q5)3

 

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example

Simplify: (2x33y)4

 

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example

Simplify: (y2)3(y2)4(y5)4

 

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For more similar examples, watch the following video.