What is the missing number in this simplified exponenetial expression: 7^? div 7^5 = 7^12
The missing number in this simplified exponential expression is 7^7.
To find the missing number, we can compare the exponents of the 7s in the equation:
7^? ÷ 7^5 = 7^12
When we divide two numbers with the same base (in this case, 7), we subtract the exponents.
So, we can rewrite the equation as:
7^(? - 5) = 7^12
For two exponential expressions with the same base to be equal, their exponents must be equal. Therefore, we can set the exponents equal to each other:
? - 5 = 12
To solve for ?, we can add 5 to both sides of the equation:
? = 12 + 5
Simplifying further:
? = 17
Therefore, the missing number is 17.
To find the missing number in this simplified exponential expression, we need to understand how exponentiation works.
Exponentiation is the process of raising a base number to the power of an exponent. In this case, we have the base number 7 raised to an unknown exponent, which we need to find.
To solve this problem, we can use the fact that when we divide two numbers with the same base, the exponents subtract. So, in this case, we know that dividing 7 raised to some exponent by 7 raised to 5 is equal to 7 raised to 12.
Mathematically, we can express this as: 7^? / 7^5 = 7^12
To simplify this equation, we subtract the exponents:
7^(? - 5) = 7^12
Since the bases are the same, we can set the exponents equal to each other:
? - 5 = 12
To isolate the missing number, we add 5 to both sides of the equation:
? = 12 + 5
Thus, the missing number in the simplified exponential expression is 17.