Solve the equation. $$ 16^{-x+22}=128^{x} $$ The solution set is $$ \{\square\} $$. Type an integer or a simplified fraction. Use a comma to separate answers as nee

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We start with the equation
$$
16^{-x+22}=128^x.
$$
Express $$16$$ and $$128$$ as powers of $$2$$:
$$
16 = 2^4 \quad \text{and} \quad 128 = 2^7.
$$
Substitute these into the equation:
$$
(2^4)^{-x+22} = (2^7)^x.
$$
Apply the power of a power rule:
$$
2^{4(-x+22)} = 2^{7x}.
$$
Since the bases are the same, equate the exponents:
$$
4(-x+22) = 7x.
$$
Distribute the 4:
$$
-4x + 88 = 7x.
$$
Combine like terms:
$$
88 = 7x + 4x,
$$
$$
88 = 11x.
$$
Solve for $$x$$:
$$
x = \frac{88}{11} = 8.
$$
The solution set is $$\{8\}$$.
The solution is $$ x = 8 $$.

Solve the equation.

The solution set is .
Type an integer or a simplified fraction. Use a comma to separate answers as nee

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Solve the equation. The solution set is . Type an integer or a simplified fraction. Use a comma to separate answers as nee