Apply the Properties of Integer Exponents to generate equivalent expressions to (4(3) ⋅ 7(−2))(−5)/7(9) ⋅ 4(−13)

Question

with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)

Answer 1

To solve the expression \((4(3) \cdot 7^{-2})(-5)/7^{9} \cdot 4^{-13}\) using the properties of integer exponents, we'll follow these steps:

1. Rewrite using positive exponents:

   • The expression can be rewritten as: \[ \frac{4^3 \cdot 7^{-2} \cdot (-5)}{7^{9} \cdot 4^{-13}} \]
   • To eliminate negative exponents, we can use the property \(a^{-n} = \frac{1}{a^{n}}\): \[ = \frac{4^3 \cdot 7^{-2} \cdot (-5)}{7^{9} \cdot \frac{1}{4^{13}}} \] \[ = 4^3 \cdot 7^{-2} \cdot (-5) \cdot 4^{13} \cdot 7^{-9} \]
   • Combine the terms: \[ = (-5) \cdot 4^{3 + 13} \cdot 7^{-2 - 9} \] \[ = (-5) \cdot 4^{16} \cdot 7^{-11} \] \[ = -5 \cdot \frac{4^{16}}{7^{11}} \]

2. Rewrite using positive exponents:

   • To express this with only positive exponents: \[ = \frac{-5 \cdot 4^{16}}{7^{11}} \]

3. Express the final fraction:

   • Thus, we can write the simplified expression as: \[ = -\frac{5 \cdot 4^{16}}{7^{11}} \]

4. Final Result:

   • The final answer is: \[ -\frac{5 \cdot 4^{16}}{7^{11}} \]

The expression does not contain any remaining negative exponents, and is in the form of a simplified fraction. The answer is \(-\frac{5 \cdot 4^{16}}{7^{11}}\).