Questions: 0.3 ∛1000 - 5 ⋅ ∛⁸256 + 6 ⋅ (-∛¹⁶6)^16

Transcript text: 1) $0.3 \sqrt[3]{1000}-5 \cdot \sqrt[8]{256}+6 \cdot(-\sqrt[16]{6})^{16}$

Solution

To solve the given expression, we need to break it down into smaller parts and evaluate each part separately. Specifically, we need to:

Calculate the cube root of 1000 and multiply it by 0.3.
Calculate the 8th root of 256 and multiply it by -5.
Calculate the 16th root of 6, raise it to the power of 16, and then multiply it by 6.
Sum the results of the above calculations.

Step 1: Calculate $0.3 \sqrt[3]{1000}$

We need to find the cube root of 1000 and then multiply it by 0.3: \[ 0.3 \sqrt[3]{1000} = 0.3 \times 10 = 3 \]

Step 2: Calculate $-5 \cdot \sqrt[8]{256}$

We need to find the 8th root of 256 and then multiply it by -5: \[ -5 \cdot \sqrt[8]{256} = -5 \cdot 2 = -10 \]

Step 3: Calculate $6 \cdot (-\sqrt[16]{6})^{16}$

We need to find the 16th root of 6, raise it to the power of 16, and then multiply it by 6: \[ (-\sqrt[16]{6})^{16} = -6 \] \[ 6 \cdot (-6) = -36 \]

Step 4: Sum the Results

Now, we sum the results from the previous steps: \[ 3 + (-10) + (-36) = 3 - 10 - 36 = -43 \]

\[ \boxed{-43} \]

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