what is the missing number in this simplified exponential expression 7 to the power of ? divided by 7 to the power of 5 = 7 to the power of 12
The missing number in this simplified exponential expression is 7.
To find the missing exponent, we can use the property of exponents which states that when you divide two powers with the same base, you subtract their exponents.
In this case, we know:
7^? / 7^5 = 7^12
To find the missing exponent, we subtract the exponent of 7^5 from the exponent of 7^?, so we have:
? - 5 = 12
To solve for ?, we can add 5 to both sides of the equation:
? = 12 + 5
? = 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 exponent property that states:
"Any base raised to the power of a number subtracted by the same base raised to another power equals the base raised to the difference of the powers."
Using this property, we can set up the equation:
7^(x - 5) = 7^12
Now, we can equate the exponents:
x - 5 = 12
To find the value of 'x', we can solve this simple equation by isolating 'x' on one side:
x = 12 + 5
x = 17
Therefore, the missing number in the simplified exponential expression is 17.