Question

Select the expressions that are equivalent to the expression below

Answer 1

$(\frac{750}{512} )^{\frac{1}{3}}$

We know that,

$(\frac{x}{y})^{ \frac{1}{n}} =\sqrt[n]{(\frac{x}{y}) }$ = $\frac{\sqrt[n]{x}}{\sqrt[n]{y}}$

So, the equivalents we have are

$(\frac{750}{512} )^{\frac{1}{3}} = \frac{\sqrt{750}}{\sqrt[3]{512}} = \sqrt[3](\frac{750}{512} ) = \frac{5}{8} \sqrt[3]{6}$

Answer 2

Answer:

(A), (B) and (E)

Step-by-step explanation:

The given expression is:

$(\frac{750}{512})^\frac{1}{3}$

We know that $(\frac{x}{y})^\frac{1}{n}=\sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}$

(A) The given option is:

$\frac{\sqrt[3]{750}}{\sqrt[3]{512}}$

Now, the given expression can be solved as:

$(\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}$

which is equivalent to the given option, thus this option is correct.

(B) The given option is:

$\sqrt[3]{\frac{750}{512}}$

Now, the given expression can be solved as:

$(\frac{750}{512})^\frac{1}{3}=\sqrt[3]{\frac{750}{512}}$

which is equivalent to the given option, thus this option is correct.

(C) The given option is:

$\frac{5}{8}$

Now, the given expression can be solved as:

$(\frac{750}{512})^\frac{1}{3}=(\frac{375}{256})^\frac{1}{3}$

which is not equivalent to the given option, thus this option is incorrect.

(D) The given option is:

$\frac{750}{\sqrt[3]{512}}$

Now, the given expression can be solved as:

$(\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}$

which is not equivalent to the given option, thus this option is incorrect.

(E) The given option is:

$\frac{5}{8}\sqrt[3]{6}$

Now, the given expression can be solved as:

$(\frac{750}{512})^\frac{1}{3}=\frac{5}{8}\sqrt[3]{6}$

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:

$(\frac{750}{512})^\frac{1}{3}=\frac{\sqrt[3]{750}}{\sqrt[3]{512}}$

which is not equivalent to the given option, thus this option is incorrect.