%5E-1.jpeg "(9/7)^-1")
Understanding (9/7)^-1
In mathematics, a negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. Let's break down what (9/7)^-1 means and how to solve it.
Understanding the Concept
- Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2 is 1/2.
- Negative Exponent: A negative exponent means "take the reciprocal". So, x^-1 is the same as 1/x.
Solving (9/7)^-1
- Apply the negative exponent rule: (9/7)^-1 = 1 / (9/7)
- Simplify by dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of (9/7) is (7/9).
- Calculate: 1 / (9/7) = 1 * (7/9) = 7/9
Therefore, (9/7)^-1 is equal to 7/9.
Key Points to Remember
- Any number raised to the power of -1 is equal to its reciprocal.
- When dealing with fractions raised to a negative exponent, remember to take the reciprocal of the entire fraction.
By understanding these concepts, you can easily calculate the value of any expression with a negative exponent.