What is the missing value?
\[ 7^{\_\_} / 7^5 = 7^{-2} \]
A. 7
B. 3
C. -3
D. -7
Answer (3)
The correct answer is B. It's because the result of dividing exponentations with the same bases (other than 0) is always the same base powered to the difference of all the exponentations. The formula is:
a m a n = a n − m
In this situation it's:
7 5 7 3 = 7 − 2 because 3 - 5 = -2.
To find the missing value in the equation, we can use the rule of exponents. The missing value is 3. ;
The missing value is 3, which corresponds to option B. This is found by using the property of exponents that relates to division. After calculating, we confirmed that our answer is consistent with the original equation.
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