Decoding the Enigma- The Intriguing Result of Negative 3 to the Power of Negative 3

What is negative 3 to the negative 3rd power? This question might seem complex at first glance, but it can be easily solved by understanding the properties of exponents. In mathematics, exponents represent the number of times a base number is multiplied by itself. In this case, the base number is -3, and the exponent is -3. Let’s delve into the concept and find out the answer step by step.

In general, when dealing with negative numbers raised to a negative exponent, we can convert the expression into a positive exponent by taking the reciprocal of the base number. This means that (-3)^(-3) can be rewritten as (1/(-3))^3. By doing this, we have transformed the negative exponent into a positive one, making it easier to calculate.

Now, let’s calculate the value of (1/(-3))^3. First, we find the reciprocal of -3, which is -1/3. Next, we raise this reciprocal to the power of 3:

(-1/3)^3 = (-1)^3 / (3)^3

The cube of -1 is -1, and the cube of 3 is 27. Therefore, we have:

(-1)^3 / (3)^3 = -1 / 27

Thus, the answer to the question “What is negative 3 to the negative 3rd power?” is -1/27. This demonstrates the importance of understanding exponent properties and how they can be applied to solve complex mathematical problems.