1 Answer

Simmons · Answer 1 · 2020-05-05T06:00:40+0000

For this case we must simplify the following expression:

$\sqrt [3] {8x ^ 5 * y ^ 6}$

We know that:

8 = 2 ^ 3

x ^ 5 = x ^ 3 * x ^ 2 (To multiply powers of the same base, place the same base and add the exponents)

In addition, by definition of power properties we have to:

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

Rewriting the expression we have:

$\sqrt [3] {2 ^ 3 * x ^ 3 * x ^ 2 * y ^ 6} =$

Applying the mentioned property we have:

$2 ^ {\frac {3} {3}} * x ^ {\frac {3} {3}} * y ^ {\frac {6} {3}} \sqrt [3] {x ^ 2} =\\2xy ^ 2 \sqrt [3] {x ^ 2}$

Answer:

$2xy ^ 2 \sqrt [3] {x ^ 2}$

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