Final answer:
The missing term in the given expression is x^158, as we simplify the expression using the rules of exponents by adding and multiplying them appropriately. Since x^158 is not one of the provided options, there seems to be an error in the question or the options given.
Step-by-step explanation:
To find the missing term in the expression (x^12)^5 x (x^-2)^9 times the missing term, equals (x^40)^5, we need to remember the rules for exponents.
First, let's simplify the parts of the expression we do have:
- (x^12)^5 = x^(12*5) = x^60
- (x^-2)^9 = x^(-2*9) = x^-18
Now we have x^60 x x^-18 times the missing term equals (x^40)^5, which further simplifies to:
- (x^40)^5 = x^(40*5) = x^200
So, x^60 x x^-18 x (missing term) = x^200. When multiplying exponents with the same base, we can add the exponents:
x^(60 + (-18) + missing exponent) = x^200
Therefore,
60 - 18 + missing exponent = 200
Simplifying that we get:
missing exponent = 200 - 60 + 18
missing exponent = 158
So the missing term in the expression is x^158, which is not one of the provided options. Therefore, there may be an error in the question or the provided options.