Question
Exponent Rules Unit Test
5 of 155 of 15 Items
Question
What is the missing number in this simplified exponential expression: 7?รท75=712
?(1 point)
Answers
GPT-4o mini
To find the missing number in the expression \( 7^? \div 7^5 = 7^{12} \), we can use the quotient rule of exponents, which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to the given equation:
\[
7^? \div 7^5 = 7^{? - 5}
\]
Setting that equal to \( 7^{12} \), we have:
\[
7^{? - 5} = 7^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
Now, solve for \( ? \):
\[
? = 12 + 5 = 17
\]
Thus, the missing number is \( 17 \).
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to the given equation:
\[
7^? \div 7^5 = 7^{? - 5}
\]
Setting that equal to \( 7^{12} \), we have:
\[
7^{? - 5} = 7^{12}
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
? - 5 = 12
\]
Now, solve for \( ? \):
\[
? = 12 + 5 = 17
\]
Thus, the missing number is \( 17 \).