Question

Which expression is equivalent to 200k¹5, if k + 0?

O A. 2k¹225
O B. 2k5 25
O c.
O D.
8k5/25
8kv/25

Answer 1

Answer: Choice B

`2k^5\sqrt[3]{25}`

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Work Shown:

`\sqrt[3]{200k^(15)}\\\\\sqrt[3]{8*25k^(5*3)}\\\\\sqrt[3]{8*25(k^5)^3}\\\\\sqrt[3]{8(k^5)^3*25}\\\\\sqrt[3]{8(k^5)^3}*\sqrt[3]{25}\\\\2k^5\sqrt[3]{25}`

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Step-by-step explanation:

The goal is to factor the radicand in such a way that we pull out perfect cube factors.

Notice that 200 = 8*25 and 8 is a perfect cube (since 2^3 = 8). It is the largest perfect cube factor of 200.

We can rewrite the k^15 as k^(5*3) which is equivalent to (k^5)^3

Once these perfect cube factors are pulled out, they cancel with the cube root to get what you see above.