Select all the following expressions that are equivalent to 9 1/2.
3 1/2 x 3 1/2
6√27
27 1/3 x 3 1/2
81 1/2 x 81 1/2
729 1/6
81 1/3 x 81 1/3
81 1/4 x 81 1/4
3 1/2 x 3 1/2
81 1/3 x 81 1/3
81 1/4 x 81 1/4
Find the value of n if n√256 = 8 1/3 x 8 1/3
To find the value of n, we need to simplify the right side of the equation first.
8 1/3 x 8 1/3 = (25/3) x (25/3)
To multiply these fractions, we multiply the numerators together and the denominators together:
(25/3) x (25/3) = (25 x 25) / (3 x 3) = 625 / 9
Now we have the equation:
n√256 = 625 / 9
To find n, we need to isolate it on one side of the equation. We can do this by taking the nth root of both sides:
√256 = √(625 / 9)
The square root of 256 is 16. To simplify the right side of the equation, we can take the square root of the numerator and the denominator separately:
√(625) / √(9) = 25 / 3 = n
So, n = 25/3.