Which of the following is the equivalent expression to (13^−7)^0 ⋅ 7^−11/7^−9 , generated by applying the properties of exponents?

Answer 1

To simplify the expression \((13^{-7})^0 \cdot \frac{7^{-11}}{7^{-9}}\), we can apply the properties of exponents step by step.

1. Applying the Zero Exponent Rule: Any non-zero number raised to the power of 0 is equal to 1. Therefore, we simplify \((13^{-7})^0\) to: \[ (13^{-7})^0 = 1 \]

2. Simplifying the Fraction: Next, we'll simplify the fraction \(\frac{7^{-11}}{7^{-9}}\) using the quotient rule of exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\): \[ \frac{7^{-11}}{7^{-9}} = 7^{-11 - (-9)} = 7^{-11 + 9} = 7^{-2} \]

3. Combining the Results: Now, substitute back into the expression: \[ 1 \cdot 7^{-2} = 7^{-2} \]

Thus, the equivalent expression is: \[ \boxed{7^{-2}} \]