%5E-1-without-exponent.jpeg "(2/7)^-1 Without Exponent")
Understanding (2/7)^-1 Without Exponents
The expression (2/7)^-1 might seem intimidating at first glance, especially if you're not comfortable working with exponents. However, understanding the concept of negative exponents makes this calculation surprisingly simple.
The Power of Negative Exponents
In essence, a negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. In other words:
x^-n = 1 / x^n
Applying this to our expression (2/7)^-1, we get:
(2/7)^-1 = 1 / (2/7)^1
Simplifying the Expression
Since any number raised to the power of 1 is simply itself, we can further simplify:
1 / (2/7)^1 = 1 / (2/7)
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/7 is 7/2. Therefore:
1 / (2/7) = 1 * (7/2) = 7/2
The Final Answer
Therefore, (2/7)^-1 without exponents is equal to 7/2.