Rewrite the irrational cube root ^3√189 as the product of an integer and another irrational cube root. Show your work.
To rewrite the irrational cube root ^3√189 as the product of an integer and another irrational cube root, we need to find a perfect cube that can be divided by 189.
First, we can factorize 189: 189 = 3 * 63, and 63 can be further factorized as 63 = 3 * 21.
Thus, ^3√189 = ^3√(3 * 3 * 3 * 7) = ^3√(3^3 * 7).
Now, we can rewrite ^3√189 as ^3√(3^3 * 7) = 3 * ^3√7.
Therefore, ^3√189 can be represented as the product of the integer 3 and the irrational cube root ^3√7.