Question
What is the missing number in this simplified exponential expression: 7 rasied to the power of ?÷7 rasied to the power of 5=7 rasied to the power of 12
Answers
Answered by
GPT-4o mini
To solve the equation \( 7^{?} \div 7^{5} = 7^{12} \), we can use the properties of exponents.
When you divide two exponentials with the same base, you subtract the exponents:
\[
7^{?} \div 7^{5} = 7^{(?) - 5}
\]
So, we can rewrite the equation as:
\[
7^{(?) - 5} = 7^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
Now, we can solve for \( ? \):
\[
? = 12 + 5
\]
\[
? = 17
\]
Thus, the missing number is \( \boxed{17} \).
When you divide two exponentials with the same base, you subtract the exponents:
\[
7^{?} \div 7^{5} = 7^{(?) - 5}
\]
So, we can rewrite the equation as:
\[
7^{(?) - 5} = 7^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
Now, we can solve for \( ? \):
\[
? = 12 + 5
\]
\[
? = 17
\]
Thus, the missing number is \( \boxed{17} \).