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 answer

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.