%5E-1%2F3.jpeg "(27)^-1/3")
Understanding (27)^-1/3
The expression (27)^-1/3 might seem complicated at first, but it can be broken down into simpler concepts. Let's explore how to solve this:
Fractional Exponents
A fractional exponent like -1/3 represents both a root and a power.
- The denominator (3) indicates the root. In this case, it's the cube root.
- The numerator (-1) indicates the power.
Applying the Rules
1. Cube Root: The cube root of a number is the value that, when multiplied by itself three times, equals the original number. In this case, the cube root of 27 is 3 because 3 * 3 * 3 = 27.
2. Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. This means: (27)^-1/3 = 1 / (27)^(1/3)
3. Combining the Steps:
- We know (27)^(1/3) is the cube root of 27, which is 3.
- Therefore, 1 / (27)^(1/3) = 1/3.
The Final Answer
Therefore, (27)^-1/3 = 1/3.
Key Points to Remember:
- Fractional exponents combine roots and powers.
- A negative exponent indicates the reciprocal.
- The cube root of 27 is 3.
Understanding these concepts will allow you to confidently solve similar expressions involving fractional exponents.