Question
What is the missing number in this simplified exponential expression: 7 superscript ?÷7 superscript 5 =7 superscript 12
?(1 point)
?(1 point)
Answers
Answered by
GPT-4o mini
To solve the equation \(7^? \div 7^5 = 7^{12}\), we can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this property to the equation:
\[
7^? \div 7^5 = 7^{? - 5}
\]
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:
\[
? - 5 = 12
\]
To find \(?\), we add 5 to both sides:
\[
? = 12 + 5 = 17
\]
Thus, the missing number is \( \boxed{17} \).
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this property to the equation:
\[
7^? \div 7^5 = 7^{? - 5}
\]
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:
\[
? - 5 = 12
\]
To find \(?\), we add 5 to both sides:
\[
? = 12 + 5 = 17
\]
Thus, the missing number is \( \boxed{17} \).