Find the missing value for
7^16/7^? = 7^7
? =
The missing value is 9.
To find the missing value, we need to simplify the equation by applying the properties of exponents.
According to the property of exponents, when dividing powers with the same base, we subtract the exponents.
So, 7^16/7^? can be simplified as 7^(16 - ?).
We are given that 7^16/7^? = 7^7.
Therefore, we can write the equation as 7^(16 - ?) = 7^7.
Since the bases are the same (7), we can equate the exponents:
16 - ? = 7.
To find the missing value (?), we need to solve this equation for ?.
Subtracting 16 from both sides of the equation gives:
-? = 7 - 16
Simplifying further:
-? = -9.
Now, to solve for ?, multiply both sides of the equation by -1:
-1 * -? = -1 * -9
This gives:
? = 9.
Therefore, the missing value is 9.
To find the missing value represented by '?', we can solve the equation:
7^16 / 7^? = 7^7
To solve this equation, we can use the properties of exponents. When dividing two exponential expressions with the same base, we subtract the exponents. Therefore, we can rewrite the equation as:
7^(16 - ?) = 7^7
Since the bases (7) are the same on both sides of the equation, we can equate the exponents:
16 - ? = 7
Now, solve for '?':
16 - ? = 7
-? = 7 - 16
-? = -9
Divide both sides of the equation by -1 to solve for '?':
? = (-9) / (-1)
? = 9
So, the missing value '?', which makes the equation true, is 9.