Question

What is the missing number in this simplified exponential expression: 7exponent?÷7exponent5=7exponent12?

Answer 1

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

First, we know that when we divide two numbers with the same base, we can subtract the exponents:

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

So we can rewrite the equation as:

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

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

\[
x - 5 = 12
\]

To solve for \(x\), add 5 to both sides:

\[
x = 12 + 5
\]

\[
x = 17
\]

Therefore, the missing number is \( \boxed{17} \).