What is the missing number in this simplified exponential expression: 7^? ÷ 7^5 = 7^12?
The missing number in this simplified exponential expression is 7.
To find the missing number in the simplified exponential expression, we can use the properties of exponents.
The property we'll use states that when dividing two numbers with the same base, we subtract the exponents.
In this case, we have:
7^? ÷ 7^5 = 7^12
According to the property, we subtract the exponents:
7^(? - 5) = 7^12
To make both sides of the equation equal, the exponents must be equal as well:
? - 5 = 12
Now, we isolate the variable ? by adding 5 to both sides:
? = 12 + 5
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
To find the missing number in this simplified exponential expression, we can use the property of division with the same base. According to the property, when dividing exponential expressions with the same base, we subtract the exponents.
In this case, we have the equation:
7^? ÷ 7^5 = 7^12
To find the missing number represented by the question mark, we subtract the exponent of the denominator from the exponent of the numerator.
So, we have:
7^? - 7^5 = 7^12
To simplify further, we can rewrite 7^? as 7^5 + 7^? (using the property that adding exponents with the same base corresponds to multiplying the exponentiated values).
Therefore:
(7^5 + 7^?) - 7^5 = 7^12
By canceling out the 7^5 on both sides, we get:
7^? = 7^12
Since the bases are the same on both sides of the equation, we can conclude that the exponent ? is equal to 12.