(1/9)^-3

2 min read Jun 16, 2024
(1/9)^-3

Understanding (1/9)^-3

In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive power. Let's break down how to calculate (1/9)^-3.

The Power of Reciprocals

  • Reciprocal: The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 9 is 1/9.
  • Negative Exponent: A negative exponent means we take the reciprocal of the base raised to the positive power.

Therefore, (1/9)^-3 can be rewritten as:

(1/9)^-3 = (1/(1/9))^3

Simplifying the Equation

  • Reciprocal of 1/9: The reciprocal of 1/9 is 9/1, which is simply 9.

Now we have:

(1/9)^-3 = (9)^3

Final Calculation

  • 9^3: 9 multiplied by itself three times (9 * 9 * 9). This equals 729.

Therefore, (1/9)^-3 = 729.

Conclusion

By understanding the concepts of reciprocals and negative exponents, we can easily solve expressions like (1/9)^-3. Remember that a negative exponent indicates taking the reciprocal of the base raised to the positive power.

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