What is the missing number in the simplified exponential expression: 7^? ÷ 7^5 = 7^12
The missing number in the simplified exponential expression is 7^7.
To find the missing number in the given exponential expression, we can use the properties of exponents.
According to the property of exponentiation, when two exponents with the same base are divided, we subtract the exponents.
So, in this case, we have:
7^x ÷ 7^5 = 7^12
Using the property, we subtract the exponents:
7^(x-5) = 7^12
For two exponents to be equal, the bases must be equal as well. Therefore, we equate the exponents:
x - 5 = 12
To isolate the variable, we add 5 to both sides of the equation:
x = 12 + 5
x = 17
Therefore, the missing number in the simplified exponential expression is 17.
To find the missing number in the simplified exponential expression, we can use the properties of exponentiation.
In this case, we have an equation involving powers of 7. We know that dividing two exponential expressions with the same base subtracts the exponents. Therefore, we can rewrite the given equation as:
7^? ÷ 7^5 = 7^12
Now, using the property of division for exponents, we subtract the exponents:
7^(? - 5) = 7^12
Since the bases are the same (7), we can equate the exponents:
? - 5 = 12
To find the missing number, we solve this equation for the variable ?:
? = 12 + 5
? = 17
So, the missing number in the simplified exponential expression is 17.