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

1 answer

To solve the expression \(\frac{7^x}{7^5} = 7^{12}\), we can use the properties of exponents.

According to the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can rewrite the left side:

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

Now, we set this equal to the right side:

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

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

\[ x - 5 = 12 \]

Now, we solve for \(x\):

\[ x = 12 + 5 = 17 \]

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