Examine the Power of Inversion: Simplify 300^-4 x (1/300)^-4

When you have a negative exponent on a fraction, it flips the fraction and makes the exponent positive. So $\left(\frac{1}{300}\right)^{-4} = \left(\frac{300}{1}\right)^4 = 300^4$!

Use $a^m \cdot a^n = a^{m+n}$. In our problem: $300^{-4} \cdot 300^4 = 300^{-4+4} = 300^0$. Add the exponents when multiplying!

This is a fundamental rule: $a^0 = 1$ for any non-zero number. Think of it as $\frac{a^n}{a^n} = a^{n-n} = a^0 = 1$. Any number divided by itself equals 1!

Yes! You could rewrite $300^{-4} = \frac{1}{300^4}$ and get $\frac{1}{300^4} \cdot 300^4 = 1$. But using the reciprocal rule is usually faster and cleaner.

The answer would still be 1! For any non-zero number a: $a^{-n} \cdot \left(\frac{1}{a}\right)^{-n} = a^{-n} \cdot a^n = a^0 = 1$. The pattern always works!