What is the missing number in this simplified exponential expression: 7 to the ? power divided by 7 to the fifth power = 7 to the twelfth power

Answer 1

To solve for the missing number in the expression \( \frac{7^x}{7^5} = 7^{12} \), we can use the property of exponents that states:

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

Applying this property to our expression, we have:

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

So we can rewrite the equation as:

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

Since the bases are the same (7), we can set the exponents equal to each other:

\[ x - 5 = 12 \]

Now, we can solve for \( x \):

\[ x = 12 + 5 = 17 \]

Thus, the missing number in the expression is:

\[ \boxed{17} \]