For this case, we must simplify the following expression:
[tex]\sqrt [3] {\frac {4x} {5}}[/tex]
For this, we follow the steps below:
We rewrite the expression as:
[tex]\frac {\sqrt [3] {4x}} {\sqrt [3] {5}}[/tex]
We multiply by:
[tex]\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} =[/tex]
We have by definition of multiplication of powers of equal base that:
[tex]a ^ m * a ^ n = a ^ {m + n}[/tex]
So:
[tex]\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {\sqrt [3] {5}) ^ 3} =\\\frac {\sqrt [3] {4x} * (\sqrt [3] {5}) ^ 2} {5} =[/tex]
We know that:
[tex](\sqrt [3] {5}) ^ 2 = \sqrt [3] {5 ^ 2}[/tex]
So, we have:
[tex]\frac {\sqrt [3] {4x} * \sqrt [3] {5 ^ 2}} {5} =\\\frac {\sqrt [3] {4x} * \sqrt [3] {25}} {5} =\\\frac {\sqrt [3] {100x}} {5}[/tex]
Answer:
Option c
