Answer:
(A), (B) and (E)
Step-by-step explanation:
The given expression is:
[tex](\frac{750}{512})^\frac{1}{3}[/tex]
We know that [tex](\frac{x}{y})^\frac{1}{n}=\sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}[/tex]
(A) The given option is:
[tex]\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]
which is equivalent to the given option, thus this option is correct.
(B) The given option is:
[tex]\sqrt[3]{\frac{750}{512}}[/tex]
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=\sqrt[3]{\frac{750}{512}}[/tex]
which is equivalent to the given option, thus this option is correct.
(C) The given option is:
[tex]\frac{5}{8}[/tex]
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=(\frac{375}{256})^\frac{1}{3}[/tex]
which is not equivalent to the given option, thus this option is incorrect.
(D) The given option is:
[tex]\frac{750}{\sqrt[3]{512}}[/tex]
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]
which is not equivalent to the given option, thus this option is incorrect.
(E) The given option is:
[tex]\frac{5}{8}\sqrt[3]{6}[/tex]
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=\frac{5}{8}\sqrt[3]{6}[/tex]
which is equivalent to the given option, thus this option is correct.
(F) The given option is:
\frac{\sqrt[3]{750}}{512}
Now, the given expression can be solved as:
[tex](\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}[/tex]
which is not equivalent to the given option, thus this option is incorrect.
