A General Note: The Zero Exponent Rule of Exponents
For any nonzero real number
a, the zero exponent rule of exponents states that
Example 4: Using the Zero Exponent Rule
Simplify each expression using the zero exponent rule of exponents.
- c3c3
- x5−3x5
- (j2k)⋅(j2k)3(j2k)4
- (rs2)25(rs2)2
Solution
Use the zero exponent and other rules to simplify each expression.
- \begin{array}\text{ }\frac{c^{3}}{c^{3}} \hfill& =c^{3-3} \\ \hfill& =c^{0} \\ \hfill& =1\end{array}
- x5−3x5=====−3⋅x5x5−3⋅x5−5−3⋅x0−3⋅1−3
- (j2k)⋅(j2k)3(j2k)4=====(j2k)1+3(j2k)4(j2k)4(j2k)4(j2k)4−4(j2k)01Use the product rule in the denominator.Simplify.Use the quotient rule.Simplify.
- (rs2)25(rs2)2====5(rs2)2−25(rs2)05⋅15Use the quotient rule.Simplify.Use the zero exponent rule.Simplify.
Try It 4
Simplify each expression using the zero exponent rule of exponents.
a. t7t7
b. 2(de2)11(de2)11
c. w6w4⋅w2
d. t2⋅t5t3⋅t4
Solution