Question

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

Answer 1

Answer:

(A)$128^{x/3}$

(D)$(4(2^{1/3}))^x$

Step-by-step explanation:

We want to determine which of the expression is equivalent to:

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

By the law of indices:

$\sqrt[3]{128}=128^{1/3}\\ Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}$

Similarly:

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