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The Square of a Binomial
Solving Equations
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Rules for Nonnegative Integral Exponents

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Properties of Exponents

Example

Write the following without using a negative exponent and then simplify:

a. (-3)4

b- -34

c. (-3)-4

d. -3-4

Solution

a. Write (-3)4 as a product.

(-3)4

= (-3)(-3)(-3)(-3)
Multiply.   = 81
Thus, (-3)4 = 81.  
b. -34 is the opposite of 34.

-34

= -(34)
Write 34 as a product.   = -(3 · 3 · 3 · 3)
Multiply.   = -81
So, -34 = -81.  
c. Use the definition

(-3)-4

Write (-3)4 as a product.  
Multiply.  
Thus,    
d. -3-4 is the opposite of 3-4. That is, -3-4 = -(3-4 )  
Use the definition

-(3-4 )

Write 34 as a product.  
Multiply.  
Thus,