Hi there, as mentioned in the title, I have doubts about question 19 in the quiz.
In his solution, Greg mentions that a raised to the power of b will not always lead to a negative number. However, to validate his hypothesis, he shows (a) raised to the power of b, which is very different from just raising a (without parentheses) to the power of b.
Say, a is -2 and b is -4. -2 raised to the power of -4 will give us 1/-16 as the minus remains unaffected by the exponent (as there are no parentheses).
Looking forward to hearing your thoughts.
(-2)^{-4} = \frac{1}{2^4} = \frac{1}{16} > 0
That’s only true if we put the numbers in parentheses. But the answer choice is without parentheses. A raised to the power of b will always get us a negative value, if a is negative and without parentheses
Put it this way: If I put a = -2 and b = 4, it is the same thing as multiplying -2 four times. That is positive.
If I type -2 raised to the power of 4 in the calculator, it gives me -16. I understand your point but that holds only true if the -2 is in parentheses, otherwise the negative sign remains unaffected by the even exponent
