Which expression is equivalent to
Answer

To simplify the expression , we start by dealing with the inner part. Dividing two powers with the same base subtracts the exponent, so we have:

Now, applying the outer exponent -1 gives:

Thus, the expression simplifies to .

For real-world application, understanding exponents is crucial in fields like science and finance. For instance, in biology, the exponential growth of populations is modeled using exponents. Similarly, investment growth can be calculated using exponential functions to forecast future values based on current rates.

Common mistakes include forgetting the rules of exponents, especially the division of them. It’s essential to remember that dividing powers of the same base means subtracting exponents, not applying the reciprocal directly without adjusting the exponents first. A quick check of your fractions can help catch these errors!