Question

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

128 Superscript StartFraction x Over 3 EndFraction

128 Superscript StartFraction 3 Over x EndFraction

(4RootIndex 3 StartRoot 1 EndRoot)x

(4 (2 Superscript one-third Baseline) ) Superscript x

(2)x

this is on edge

Answer 1

B

C

D

Explanation:

i had the final exam on edge

Answer 2

- 128 Superscript StartFraction 3 Over x EndFraction

- (4RootIndex 3 StartRoot 2 EndRoot)x

- (4 (2 Superscript one-third Baseline) ) Superscript x

Explanation:

Given the indicinal equation
`(\sqrt[3]{128} )^(x)\\`

According to one of the law of indices,

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

Applying this law to the question;

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

The following are therefore true based on the following calculation

128 Superscript StartFraction 3 Over x EndFraction

(4RootIndex 3 StartRoot 2 EndRoot)x

(4 (2 Superscript one-third Baseline) ) Superscript x