Rewrite 10^((1)/(3)) * 10^((5)/(6)) using a root
10^(1/3) * 10^(5/6) can be rewritten as 10^((1/3) + (5/6)).
Now, let's express the exponents as fractions with a common denominator:
1/3 = 2/6, and
5/6 = 5/6.
Therefore, the expression can be rewritten as 10^((2/6) + (5/6)).
Since the denominators are the same, we can combine the numerators.
So, 2/6 + 5/6 = 7/6.
Finally, the expression can be written as 10^(7/6), which is equivalent to the original expression.
To rewrite 10^((1)/(3)) * 10^((5)/(6)) using a root, we can simplify the expression as follows:
10^((1)/(3)) * 10^((5)/(6)) = (10^((1)/(3) + (5)/(6)) = 10^((2)/(6) + (5)/(6))
= 10^((7)/(6))
Since the numerator is 7 and the denominator is 6, we can rewrite 10^((7)/(6)) using a root as the 6th root of 10^7. Therefore, the expression can be written as:
10^((1)/(3)) * 10^((5)/(6)) = 6th root of 10^7
To rewrite the expression 10^((1)/(3)) * 10^((5)/(6)) using a root, we can first simplify each exponent separately.
Let's start with 10^((1)/(3)). This expression represents the cube root of 10.
Similarly, for 10^((5)/(6)), this expression represents the sixth root of 10^5.
Now, we can rewrite the expression as the cube root of 10 multiplied by the sixth root of 10^5.
In mathematical notation, this can be written as ∛10 * ∛∛∛10^5.