(16^√√256b^4)^8. ответ 4b

Let's simplify the expression step by step:

1. Start with the expression: \((16^{\sqrt{\sqrt{256}b^4}})^8\).

2. First, simplify \(\sqrt{\sqrt{256}}\): \(\sqrt{256} = 16\), and \(\sqrt{16} = 4\). Therefore, \(\sqrt{\sqrt{256}} = 4\).

3. Substitute this back into the expression: \[ (16^{4b^4})^8. \]

4. Apply the power of a power property \((a^m)^n = a^{m \cdot n}\): \[ 16^{4b^4 \cdot 8} = 16^{32b^4}. \]

5. Now, recall that \(16 = 2^4\), so: \[ 16^{32b^4} = (2^4)^{32b^4} = 2^{4 \cdot 32b^4} = 2^{128b^4}. \]

6. Since the answer is given as \(4b\), we can express \(4\) as \(2^2\): \[ 2^{128b^4} = 4b \implies 128b^4 = 2 + \log_2b. \]

However, since the direct simplification does not yield \(4b\), there seems to be a misunderstanding in the question itself or the computation of expected result.

In conclusion, the result of the expression simplifies to \(2^{128b^4}\) and does not equal \(4b\). Please check to see if there’s any context or additional information to clarify the expected result.