Question

9 min left please help

Answer 1

the answer for this question is 20 x cube by 5

Answer 2

For this case, we must simplify the following expression:

$\sqrt [3] {\frac {4x} {5}}$

For this, we follow the steps below:

We rewrite the expression as:

$\frac {\sqrt [3] {4x}} {\sqrt [3] {5}}$

We multiply by:

$\frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2}\\\frac {\sqrt [3] {4x}} {\sqrt [3] {5}} * \frac {(\sqrt [3] {5}) ^ 2} {(\sqrt [3] {5}) ^ 2} =$

We have by definition of multiplication of powers of equal base that:

$a ^ m * a ^ n = a ^ {m + n}$

So:

$\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {\sqrt [3] {5}) ^ 3} =\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {5} =$

We know that:

$(\sqrt [3] {5}) ^ 2 = \sqrt [3] {5 ^ 2}$

So, we have:

$\frac {\sqrt [3] {4x} * \sqrt [3] {5 ^ 2}} {5} =\\\frac {\sqrt [3] {4x} * \sqrt [3] {25}} {5} =\\\frac {\sqrt [3] {100x}} {5}$

Answer:

Option c