What is the missing number in this simplified exponential expression: 7^? ÷ 7^5 = 7^12
The missing number is 7.
To solve for the missing number, you can use the property of exponents that states "when dividing two powers with the same base, you subtract the exponents."
So in this case, you subtract the exponent of 7^5 from the exponent of 7^12:
7^? ÷ 7^5 = 7^12
7^(? - 5) = 7^12
Since the bases are the same (7), the exponents must also be the same. Therefore, ? - 5 = 12.
Solving for ?, you add 5 to both sides of the equation:
? - 5 + 5 = 12 + 5
? = 17
Therefore, the missing number is 17.
To find the missing number in this simplified exponential expression, we need to use some properties of exponents. The property we will apply is the quotient property of exponents, which states that when dividing two exponential expressions with the same base, we subtract the exponents.
In this case, we have 7^? ÷ 7^5 = 7^12. Since the base is the same (7), we can subtract the exponents on both sides of the equation.
On the left side, we have 7^? ÷ 7^5, and on the right side, we have 7^12. By applying the quotient property of exponents, we can subtract 5 from the unknown exponent on the left side and write the equation as 7^(? - 5) = 7^12.
Since the bases are the same, for the two exponential expressions to be equal, their exponents must be equal as well. Therefore, we have the equation ? - 5 = 12.
To find the missing number, we solve this equation for the unknown, which is denoted by the question mark (?). Adding 5 to both sides of the equation, we get:
? = 12 + 5
? = 17
Thus, the missing number in the simplified exponential expression 7^? ÷ 7^5 = 7^12 is 17.
To find the missing number in this simplified exponential expression, we need to apply the properties of exponents.
In this case, we have 7 raised to an unknown power divided by 7 raised to the power of 5, which equals 7 raised to the power of 12.
Using the property of division with exponents, we subtract the exponents when dividing the same base.
Therefore, to find the missing number, we subtract the exponent of 7^5 from the exponent of 7^12:
12 - 5 = 7
So the missing number in the given expression is 7.