Let’s analyze each expression step by step to determine if Lola is correct or not.
Expression A
Expression A is not explicitly given here, but based on the context of the question, we infer that it is simply:
[tex]\[ \left(\frac{a}{b}\right)^0. \][/tex]
Any number raised to the power of 0 is equal to 1, so:
[tex]\[ \left(\frac{a}{b}\right)^0 = 1. \][/tex]
Expression B
Expression B is more complex. Let's break it down:
[tex]\[ \left(\left(\frac{a}{b}\right)^{-4}\right)^0 \cdot \left(\left(\frac{a}{b}\right)^0\right)^{-4}. \][/tex]
We start with the first term:
[tex]\[ \left(\left(\frac{a}{b}\right)^{-4}\right)^0. \][/tex]
Any expression raised to the power of 0 is 1:
[tex]\[ \left(\left(\frac{a}{b}\right)^{-4}\right)^0 = 1. \][/tex]
Next, we look at the second term:
[tex]\[ \left(\left(\frac{a}{b}\right)^0\right)^{-4}. \][/tex]
We know from before that:
[tex]\[ \left(\frac{a}{b}\right)^0 = 1. \][/tex]
So we are left with:
[tex]\[ \left(1\right)^{-4} = 1. \][/tex]
Now we can multiply these results:
[tex]\[ 1 \cdot 1 = 1. \][/tex]
So the value of Expression B is also 1.
Therefore, both Expression A and Expression B have a value of 1.
Conclusion
Since both Expression A and Expression B have a value of 1, Lola is correct because each expression has a value of 1.
The correct explanation is:
Lola is correct because each expression has a value of 1.
