%5E-3.jpeg "(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.