(-3)^-3 Simplified

Suzhoumeite

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Jul 03, 2024

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Simplifying (-3)^-3

When dealing with exponential expressions, it's essential to understand the rules of exponents to simplify them correctly. In this article, we'll explore how to simplify the expression (-3)^-3.

What does (-3)^-3 mean?

The expression (-3)^-3 can be read as "minus three to the power of minus three." It's a negative number raised to a negative power. To simplify this expression, we need to understand the rules of exponents, particularly the rule of negative exponents.

Rule of Negative Exponents

The rule of negative exponents states that:

a^(-n) = 1/a^n

where 'a' is the base and 'n' is the exponent. This rule allows us to rewrite the expression (-3)^-3 in a more simplified form.

Simplifying (-3)^-3

Using the rule of negative exponents, we can rewrite (-3)^-3 as:

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

Now, we need to simplify the expression further. Recall that when you raise a negative number to an odd power, the result is negative. Therefore, (-3)^3 = -27. So, we can rewrite the expression as:

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

Now, we can simplify the fraction:

1/-27 = -1/27

Thus, the simplified form of (-3)^-3 is:

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

In conclusion, simplifying (-3)^-3 involves applying the rule of negative exponents and understanding the properties of negative numbers raised to odd powers. By following these steps, we can simplify the expression to -1/27.