%5E-1-without-exponent.jpeg "(7/8)^-1 Without Exponent")
Understanding (7/8)^-1 without Exponents
The expression (7/8)^-1 might seem intimidating at first glance, but it's actually quite simple to understand. Let's break it down:
The Power of Negatives
A negative exponent essentially means taking the reciprocal of the base. In other words, we flip the fraction. So:
(7/8)^-1 = 1 / (7/8)
Simplifying the Expression
Now we have a fraction divided by another fraction. To simplify this, we multiply the first fraction by the reciprocal of the second fraction:
1 / (7/8) = 1 * (8/7)
Final Result
Finally, we multiply the numerators and denominators to get our answer:
1 * (8/7) = 8/7
Therefore, (7/8)^-1 is equivalent to 8/7.
Key Takeaways
- A negative exponent indicates taking the reciprocal of the base.
- To simplify a fraction divided by a fraction, we multiply the first fraction by the reciprocal of the second fraction.
By understanding these principles, you can easily solve expressions involving negative exponents without relying on complex calculations.