Question

Which option lists an expression that is not equivalent to 43? O 0.253 0 0 253 O V16 fen

Answer 1

The expression 4^2/3 can be written in a radical form as:

`\sqrt[3]{4^2}`

in which if we apply the exponent to its base 4, the equation will become:

`\sqrt[3]{16}`

So, Option 3 is equivalent to the expression.

Let's take a look at other expressions.

`(\sqrt[3]{4})^2\Rightarrow(4^{(1)/(3)})^2\Rightarrow4^{(2)/(3)}`

Option 4 is also equivalent to the expression.

For Option 2,

`0.25^{-(2)/(3)}\Rightarrow((1)/(4))^{-(2)/(3)}`

To make the exponent positive, we take the reciprocal of 1/4 and that is 4. Hence,

`((1)/(4))^{-(2)/(3)}\Rightarrow4^{(2)/(3)}`

Option 2 is also equivalent to the given expression.

Therefore, the expression that is NOT equivalent to 4^2/3 is Option 1.