How do you simplify (8e^2/ 2e^5)^-1

To simplify , first simplify the fraction in parenthesis,

. We can simplify the numerical part by dividing both numerator and denominator by the common factor of 2:

.

The rest can be simplified by using the rules of exponents: when dividing the powers of the same base, the exponents subtract. So,

. This can also be written as , using the definition of the negative exponent: (A base raised to a negative power is the reciprocal of the same base raised to a positive power.)

Now, we also have to take the exponent -1 of this result. This can be done by again using the rules exponents:

. Here, each factor inside the parenthesis is raised to the power of (-1).

So, the original expression simplifies as

.