Question

Which of the following is the equivalent expression to (13−7)0 ⋅ 7−117−9 , generated by applying the properties of exponents?(1 point) Responses 13−772 the fraction with numerator 13 to the negative 7 power and denominator 7 squared - no response given 149 1 over 49 - no response given 13 ⋅ 79711 13 ⋅ 79711 - incorrect 71179

Answer 1

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

1. Evaluate \((13-7)^0\): Any non-zero expression raised to the power of 0 is 1. Therefore, \((13−7)^0 = 1\).

2. Combine the exponents for \(7^{-11} \cdot 7^{-9}\): When multiplying expressions with the same base, we add the exponents: \[ 7^{-11} \cdot 7^{-9} = 7^{-11 + (-9)} = 7^{-20} \]

Now, combining everything together, we have: \[ (13−7)^0 \cdot 7^{-11} \cdot 7^{-9} = 1 \cdot 7^{-20} = 7^{-20} \]

Since \(7^{-20}\) can also be expressed as \(\frac{1}{7^{20}}\), we can see if any of the options match that.

Now looking at your choices:

1. \(13^{-7} \cdot 7^2\)
2. \(\frac{1}{49}\) - this is \(\frac{1}{7^2}\), not our answer.
3. \(13 \cdot 79711\) - doesn't match.
4. \(71179\) - doesn’t correspond to our simplified form.

None of the choices seem to match with \(7^{-20}\) or \(\frac{1}{7^{20}}\). Please check the options again for any that represent \(7^{-20}\) or \(\frac{1}{7^{20}}\).

If there are any more options or information, feel free to provide it!