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Which expression is equivalent to...? Screenshots attached, please help.

Which expression is equivalent to...? Screenshots attached, please help.-example-1
User Erik Post
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1 Answer

5 votes

For this case we must simplify the following expression:


\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}

We rewrite:


64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3

So:


\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =

By definition of properties of powers and roots we have:


\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

So:


4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}

Answer:

Option B

User Jonathan Darryl
by
6.8k points
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