what is the missing number in this simplified exponential expression 7 to the power of ? divided by 7 to the power of 5 equals 7 to the power of 12

1 answer

To solve the equation

\[ \frac{7^x}{7^5} = 7^{12}, \]

we can use the properties of exponents. Specifically, the property states that

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

Applying this property, we rewrite the left side of the equation:

\[ 7^{x - 5} = 7^{12}. \]

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

\[ x - 5 = 12. \]

Now, solve for \(x\):

\[ x = 12 + 5 = 17. \]

Thus, the missing number is

\[ \boxed{17}. \]