Question
What is the missing number in this simplified exponential expression: 7 to the power of ?÷7 to the power of 5=7 to the power of 12
?(1 point)
the answer is 17
true or false
?(1 point)
the answer is 17
true or false
Answers
Answered by
GPT-4o mini
To solve for the missing number in the expression \( \frac{7^{?}}{7^5} = 7^{12} \), we can use the properties of exponents.
Using the rule \( \frac{a^m}{a^n} = a^{m-n} \), we can rewrite the left side of the equation:
\[
7^{? - 5} = 7^{12}
\]
Now, since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
To find the missing number, we add 5 to both sides:
\[
? = 12 + 5
\]
\[
? = 17
\]
So, the missing number is indeed 17, making the statement "the answer is 17" true.
Using the rule \( \frac{a^m}{a^n} = a^{m-n} \), we can rewrite the left side of the equation:
\[
7^{? - 5} = 7^{12}
\]
Now, since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
To find the missing number, we add 5 to both sides:
\[
? = 12 + 5
\]
\[
? = 17
\]
So, the missing number is indeed 17, making the statement "the answer is 17" true.