Question

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

Answer 1

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