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 \( 5^{-9} 4^{-1/2} \) with positive exponents only, we can use the property of negative exponents which states that \( a^{-n} = \frac{1}{a^n} \).

Starting with the expression:

\[ 5^{-9} 4^{-1/2} \]

We can apply the property to each part:

1. For \( 5^{-9} \): \[ 5^{-9} = \frac{1}{5^9} \]

2. For \( 4^{-1/2} \): \[ 4^{-1/2} = \frac{1}{4^{1/2}} = \frac{1}{\sqrt{4}} = \frac{1}{2} \]

Now, substituting these into the expression gives us:

\[ 5^{-9} 4^{-1/2} = \frac{1}{5^9} \cdot \frac{1}{2} \]

This can be combined into a single fraction:

\[ \frac{1}{5^9 \cdot 2} \]

Therefore, the expression equivalent to \( 5^{-9} 4^{-1/2} \) with positive exponents only is:

\[ \frac{1}{2 \cdot 5^9} \]