Question

Which expressions are equivalent to RootIndex 3 StartRoot 128 EndRoot Superscript x? Select three correct answers.

Answer 1

Step-by-step explanation:

The given expression is :

$(\sqrt[3]{128} )^x$

We need to solve the above expression.

According to one of the law of indices,  

$(\sqrt[a]{m} )^b=(\sqrt{m})^{b/a}$

Using above property,

$(\sqrt[3]{128} )^x=(128)^{x/3}\\\\=(64\times 2)^{x/3}\\\\=4(2)^{x/3}\ (\because\ \sqrt{64}=4) \\\\=4(\sqrt[3]{2})^x\\\\=4(2^{1/3})^x$

Hence, this is the required solution.