To find: the product of the three cube roots of 1 and product of the
Answer to Problem 99E
The product of the cube roots is
Explanation of Solution
Calculation:
Consider the formula
Using this formula, find all the cube roots of 1 and find their product. Then do the same for the fourth, fifth, sixth, and eighth roots of 1.
First find the values of the cube roots, which are given by
Write the expression for
This means that for
Now,
For the fourth roots,
So the product is:
After simplification, the product is
For the fifth roots,
So the product is:
After simplification, the product is 1.
For the sixth roots,
So the product is:
After simplification, the product is
For the eighth roots,
So the product is:
After simplification, the product is
In summary, the product of the cube roots is
Conclusion:
The product of the cube roots is
Chapter 8 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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