%5E-4%2F3.jpeg "(27)^-4/3")
Understanding (27)^-4/3
The expression (27)^-4/3 might seem intimidating at first glance, but it's actually quite straightforward to solve using the rules of exponents.
Here's a breakdown of the steps involved:
1. Fractional Exponents
Fractional exponents represent both roots and powers. The denominator of the fraction indicates the root, and the numerator indicates the power. In this case, the denominator is 3, implying a cube root, and the numerator is 4, indicating a power of 4.
2. Negative Exponent
A negative exponent indicates a reciprocal. Therefore, (27)^-4/3 is equivalent to 1/(27)^(4/3).
3. Simplifying the Expression
Now we can simplify the expression:
- Cube Root: The cube root of 27 is 3 (3 x 3 x 3 = 27).
- Power: 3 raised to the power of 4 is 81 (3 x 3 x 3 x 3 = 81).
- Reciprocal: 1/81
Therefore, (27)^-4/3 is equal to 1/81.
Key Takeaways
- Fractional exponents: Combine roots and powers.
- Negative exponents: Represent reciprocals.
- Simplify step-by-step: Break down complex expressions into manageable steps.
Understanding these concepts empowers you to confidently solve even more complicated expressions involving exponents.