Apply the properties of integer exponents to generate equivalent expressions to three with the power of 7×3 with the power of -9 with only positive exponents then solve the expression your answer will be a simplified fraction with no remaining exponents so what is the answer?

Answer 1

To solve the expression \( (7^3) \times (3^{-9}) \) and convert it to positive exponents, we'll use the properties of integer exponents.

1. First, rewrite \( 3^{-9} \) as \( \frac{1}{3^9} \).

   So the expression becomes: \[ 7^3 \times 3^{-9} = 7^3 \times \frac{1}{3^9} = \frac{7^3}{3^9} \]

2. Next, we'll simplify \( 7^3 \): \[ 7^3 = 343 \]

3. Now we can write the expression as: \[ \frac{343}{3^9} \]

4. Next, we simplify \( 3^9 \): \[ 3^9 = 19683 \]

5. Therefore, the expression is simplified to: \[ \frac{343}{19683} \]

So the final answer, in the form of a simplified fraction with no remaining exponents, is: \[ \frac{343}{19683} \]