What is the missing number in this simplified exponential expression:
7^?÷7^5=7^12 ?
pls help!
To solve for the missing number in this simplified exponential expression, we can use the exponent rule that states when dividing two exponential expressions with the same base, we subtract the exponents.
So, by applying this rule to the given equation:
7^? ÷ 7^5 = 7^12
We can rewrite the equation as:
7^(? - 5) = 7^12
According to the rule, the exponents on both sides must be equal.
Therefore, we have the equation:
? - 5 = 12
To solve for ?, we add 5 to both sides:
? = 12 + 5
? = 17
Therefore, the missing number in this simplified exponential expression is 17.
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You're welcome! I'm confident that the solution is correct. If you have any more questions, feel free to ask.
To find the missing number in the simplified exponential expression, first, we can write the left side of the equation using the product of powers rule, which states that when dividing two exponential expressions with the same base, you subtract the exponents:
7^? ÷ 7^5 = 7^12
Using the product of powers rule, we can subtract the exponents:
7^(? - 5) = 7^12
Now, since the base (7) is the same on both sides of the equation, we can equate the exponents:
? - 5 = 12
To solve for the missing number, we can add 5 to both sides of the equation:
? = 12 + 5
Simplifying,
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
To determine the missing number in the simplified exponential expression, you need to take into account the properties of exponents. Specifically, the property you need to apply is:
a^m ÷ a^n = a^(m - n)
In the given expression, we have:
7^? ÷ 7^5 = 7^12
Applying the exponent property, we can simplify the expression further:
7^(? - 5) = 7^12
Since the base (7) is the same on both sides of the equation, the exponents must be equal. Therefore, we have:
? - 5 = 12
Solving the equation, we can find the value of the missing number:
? = 12 + 5
? = 17
Therefore, the missing number in the simplified exponential expression is 17.