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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 Â· 3 Â· 3 Â· 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,