Sbuve that $$ (2 \sqrt{2})^{5}=32 \sqrt{2} $$

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It appears there may be a miscalculation in the statement $$ (2 \sqrt{2})^{5} = 32 \sqrt{2} $$. Let's carefully evaluate $$ (2 \sqrt{2})^{5} $$ step by step to find the correct result.

### Step 1: Express in Exponential Form
First, express each component in its exponential form using base 2:
$$
2 = 2^1 \quad \text{and} \quad \sqrt{2} = 2^{1/2}
$$
Therefore,
$$
2 \sqrt{2} = 2^1 \cdot 2^{1/2} = 2^{1 + 1/2} = 2^{3/2}
$$

### Step 2: Raise to the Power of 5
Now, raise $$ 2^{3/2} $$ to the 5th power:
$$
(2^{3/2})^{5} = 2^{(3/2) \times 5} = 2^{15/2}
$$

### Step 3: Simplify the Exponent
Break down the exponent $$ \frac{15}{2} $$:
$$
2^{15/2} = 2^{7 + 1/2} = 2^7 \cdot 2^{1/2} = 128 \cdot \sqrt{2}
$$

### Conclusion
Putting it all together:
$$
(2 \sqrt{2})^{5} = 128 \sqrt{2}
$$
Therefore, the correct evaluation is:
$$
(2 \sqrt{2})^{5} = 128 \sqrt{2}
$$
$$ (2 \sqrt{2})^{5} = 128 \sqrt{2} $$

Sbuve that

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