Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−94−12

Question

with positive exponents only.(1 point)
5−94−12=

Answer 1

To rewrite the expression \( 5^{-9} 4^{-12} \) with positive exponents, we can use the property of negative integer exponents, which states that \( a^{-n} = \frac{1}{a^n} \).

Using this property, we convert each term with a negative exponent:

\[ 5^{-9} = \frac{1}{5^9} \] \[ 4^{-12} = \frac{1}{4^{12}} \]

Now we can rewrite the entire expression:

\[ 5^{-9} 4^{-12} = \frac{1}{5^9} \cdot \frac{1}{4^{12}} = \frac{1}{5^9 \cdot 4^{12}} \]

Thus, the expression equivalent to \( 5^{-9} 4^{-12} \) with positive exponents only is:

\[ \frac{1}{5^9 \cdot 4^{12}} \]