Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9 divided by 46−12 with positive exponents only

Answer 1

To simplify the expression \( \frac{5^{-9}}{46^{-12}} \) using the property of negative integer exponents, we apply the rule that states \( a^{-n} = \frac{1}{a^n} \).

Here's how we can apply this property to the expression:

1. Rewrite the expression using the property of negative exponents:

\[ \frac{5^{-9}}{46^{-12}} = 5^{-9} \cdot 46^{12} \]

2. Now, we can rewrite \( 5^{-9} \) as \( \frac{1}{5^9} \):

\[ = \frac{46^{12}}{5^9} \]

This expression has only positive exponents:

\[ \frac{46^{12}}{5^9} \]

Thus, the final expression equivalent to \( \frac{5^{-9}}{46^{-12}} \) with positive exponents is:

\[ \frac{46^{12}}{5^9} \]