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Evaluate. (-7)⁵/³ · ( 1/56 )⁵/³ = ___

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Final answer:

To evaluate (-7)5/3 · ( 1/56 )5/3, one must first compute the 5th power of each base followed by taking the cube root and then multiply the two results. The final answer is approximately -0.0067.

Step-by-step explanation:

Let's evaluate the given expression: (-7)5/3 · (1/56)5/3. We will first deal with each part separately and then multiply the results.

First, the expression (-7)5/3 can be broken down as ((-7)5)1/3, which is the cube root of (-7) raised to the 5th power. (-7)5 equals -16,807, and its cube root is -119. Now, let's look at (1/56)5/3. Similarly, this is ((1/56)5)1/3, which is the cube root of (1/56) raised to the 5th power. (1/56)5 equals approximately 1.8 x 10-10, and its cube root is approximately 0.0000563.

Now, we multiply the two results: -119 · 0.0000563 = approximately -0.0067.

Thus, the final answer to (-7)5/3 · ( 1/56 )5/3 is approximately -0.0067.

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