Find the cube root of 81 / (root(81, 3))
O root(81, 3)
O 9
O 27
O-9
O 9
To find the cube root of 81 divided by the cube root of 81, first, simplify the expression 81 / (root(81, 3)):
81 / (root(81, 3)) = 81 / (81^(1/3))
Now, we can simplify further:
81^(1/3) (using the exponent property a / b) is equal to (81)^(1/3 - 1/1) = 81^(1/3 - 3/3) = 81^(-2/3) = 1 / 81^(2/3)
Now, we can rewrite the expression:
81 / (root(81, 3)) = 81 / (1 / 81^(2/3)) = 81 * 81^(2/3)
Simplifying the expression further:
81 * 81^(2/3) = 81^(1 + 2/3) = 81^(3/3 + 2/3) = 81^(5/3)
Now, let's calculate the cube root of 81^(5/3):
cube root of 81^(5/3) = (81^(5/3))^(1/3) = 81^(5/3 * 1/3) = 81^(5/9)
Therefore, the cube root of 81 / (root(81, 3)) is 81^(5/9) which cannot be simplified further.
So, the correct answer is O 81^(5/9).
To find the cube root of 81 divided by the square root of 81, we can simplify the expression first.
The cube root of 81 is the number that, when multiplied by itself two times, equals 81. In this case, the cube root of 81 is 4 since 4 * 4 * 4 = 81.
Next, we can simplify the denominator, which is the square root of 81. The square root of 81 is the number that, when multiplied by itself, equals 81. Therefore, the square root of 81 is 9 since 9 * 9 = 81.
Now, we can substitute these values back into the original expression to find the cube root:
81 / (root(81, 3)) = 81 / 9 = 9.
So, the cube root of 81 divided by the square root of 81 is 9.
The correct option is: O 9.