How will you apply the zero and negative exponent into a real life situation?

Answer 1

One example is in units of measurement. When you tune your car engine, what are the physical units of RPM? 1 revolution per minute has units of "per minute" which means 1/minutes, which is abbreviated min^-1. You ofte see density expressed in kg*m^-3. And so on.

Very large numbers and very small (i.e., close to zero) numbers are usually expressed in scientific notation using powers of 10. Multiply and divide become simply add and subtract, greatly simplifying calculation (by hand or electronically). Exponents often "cancel out" to leave a final power of zero or small positive or negative exponents. Computations often require flipping the sign of the exponent. In chemistry, e.g., Avogadro's number is 6x10^23 molecules per mole. So you automatically know that a single molecule contains (1/6)x10-23 moles.

The universe -- including our human "real world" -- spans so many powers of 10 that exponential notation is inevitable. The human scale -- how we experience the world -- lies roughly in the middle between size of the universe (largest positive powers of 10) and sub-quantum Planck realm (largest negative powers of 10). There's nothing mysterious or exotic about negative powers, compared to positive ones. Think of it as left versus right of zero (or 1 on a log scale) -- no real preference due to symmetry.

Whether you feel mathematics is invented or discovered, it's clear that negative numbers are necessary for a full description of our physical world. The same is true of negative exponents.