%5E1%2F3.jpeg "(27/64)^1/3")
Simplifying the Cube Root of (27/64)
In mathematics, finding the cube root of a number is the same as finding a number that, when multiplied by itself three times, equals the original number. In this case, we're looking to simplify the expression (27/64)^(1/3).
Understanding the Properties
To simplify this expression, we can use the following property of exponents:
(a/b)^n = a^n / b^n
Applying this property, we can rewrite our expression:
(27/64)^(1/3) = 27^(1/3) / 64^(1/3)
Finding the Cube Roots
Now, we need to find the cube roots of 27 and 64:
- The cube root of 27 is 3, because 3 * 3 * 3 = 27
- The cube root of 64 is 4, because 4 * 4 * 4 = 64
The Simplified Result
Substituting these values back into our expression, we get:
(27/64)^(1/3) = 3/4
Therefore, the simplified form of (27/64)^(1/3) is 3/4.