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.

$(\sqrt[3]{4})^2\Rightarrow(4^{\frac{1}{3}})^2\Rightarrow4^{\frac{2}{3}}$

Option 4 is also equivalent to the expression.

For Option 2,

$0.25^{-\frac{2}{3}}\Rightarrow(\frac{1}{4})^{-\frac{2}{3}}$

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

$(\frac{1}{4})^{-\frac{2}{3}}\Rightarrow4^{\frac{2}{3}}$

Option 2 is also equivalent to the given expression.

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