%5E-2.jpeg "(1/6)^-2")
Understanding (1/6)^-2
The expression (1/6)^-2 might look intimidating at first, but it's actually quite straightforward to solve. Let's break it down:
The Power of a Power
The key here lies in understanding the power of a power rule in exponents. This rule states that:
(a^m)^n = a^(m*n)
In our case, we have (1/6)^-2. Applying the rule, we get:
(1/6)^-2 = (1/6)^(-1 * 2) = (1/6)^(-2)
Negative Exponents
Now, we encounter a negative exponent. Remember that a negative exponent means taking the reciprocal of the base raised to the positive version of the exponent.
(1/6)^-2 = 1 / (1/6)^2
Simplifying the Expression
Finally, we can calculate the result:
- (1/6)^2 = (1/6) * (1/6) = 1/36
- 1 / (1/36) = 36
Therefore, (1/6)^-2 is equal to 36.
Conclusion
By applying the rules of exponents, we successfully simplified the expression (1/6)^-2. Remember to use the power of a power rule and the definition of negative exponents to solve similar problems.