So far, we have only seen integer exponents, but fractional exponents exist too. Using your knowledge of exponential laws, determine the value of ​6431​.​
Solution:
We want to find ​641/3. Recall the law of exponents
​
(an)m=anm
​
and set
​
x=641/3.
​
Then
​
x3=(641/3)3=64(1/3)â‹…3=641=64
​
so ​x​ is a number whose cube is 64. Since ​43=64, we conclude
​
641/3=4.
​
Exponents & Logarithms (Lesson 2/4)
Radicals and Roots
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Discussion
So far, we have only seen integer exponents, but fractional exponents exist too. Using your knowledge of exponential laws, determine the value of ​6431​.​
Solution:
We want to find ​641/3. Recall the law of exponents
​
(an)m=anm
​
and set
​
x=641/3.
​
Then
​
x3=(641/3)3=64(1/3)â‹…3=641=64
​
so ​x​ is a number whose cube is 64. Since ​43=64, we conclude