which of the following is the equivalent expression to (13^-7)^0 x 7^11/7^9 generated by applying the properties of exponents

Answer 1

To simplify the expression \((13^{-7})^0 \times \frac{7^{11}}{7^{9}}\) using the properties of exponents, we can follow these steps:

1. Apply the property of exponents that states anything raised to the power of 0 is 1: \[ (13^{-7})^0 = 1 \]

2. Now, use the property of exponents for division \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{7^{11}}{7^{9}} = 7^{11 - 9} = 7^{2} \]

3. Putting it all together: \[ 1 \times 7^2 = 7^2 \]

Thus, the equivalent expression to \((13^{-7})^0 \times \frac{7^{11}}{7^{9}}\) is: \[ \boxed{7^2} \]