What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12

?(1 point)

1 answer

To solve for the missing number in the expression \( 7^? ÷ 7^5 = 7^{12} \), we can use the properties of exponents.

The division of powers with the same base can be expressed as:

\[ \frac{7^a}{7^b} = 7^{a-b} \]

So we can rewrite the left side:

\[ 7^? ÷ 7^5 = 7^{? - 5} \]

Now our equation looks like this:

\[ 7^{? - 5} = 7^{12} \]

Since the bases are the same, we can set the exponents equal to each other:

\[ ? - 5 = 12 \]

Now, solve for \( ? \):

\[ ? = 12 + 5 \] \[ ? = 17 \]

Therefore, the missing number is \( 17 \).