what is the missing number in this simplified exponential expression: 7^? divided by 7^5 =7^12

1 answer

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

The property states that:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Applying this property to our expression, we have:

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

So, the equation can be rewritten as:

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

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

\[ ? - 5 = 12 \]

Now, solving for \( ? \):

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

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