Question

Find the missing exponent.
5
11
5
?
=
5
4
5
?

5
11

​
=5
4
Exponent only in the answer box

Answer 1

To solve for the missing exponent, we can set up the expression in terms of powers of 5.

From the provided information, we have:

\[
5^{11} \times 5^? = 5^4 \times 5^?
\]

Using the property of exponents that states \(a^m \times a^n = a^{m+n}\), we can rewrite both sides:

\[
5^{11 + ?} = 5^{4 + ?}
\]

Since the bases are the same, we can equate the exponents:

\[
11 + ? = 4 + ?
\]

Now, we can subtract \(?\) from both sides:

\[
11 = 4
\]

This equation doesn't make sense as-is, which implies that there must be a cancellation of exponents.

To find the missing exponent that makes both sides equal, we can remove \(?\) completely and focus on known values:

By isolating the exponents without systematic conflict, we can determine it isn’t necessary to associate them with unknowns since they would lead to \(11 = 4\).

For a valid comparison, we require them to equal a portion controlled fundamentally:

Thus, we can see the missing exponent can effectively accommodate the equation formatting:
Starting symmetry suggests:

- From exponent balance, we can shift:
\[(11 - 4) = ? \]
\[ = 7 \]

Hence, the missing exponent required in the context serves:

**7**