Question

Which of the following best defines 2 to the power of 2 over 3?

A.) Cube root of 4
B.) Square root of 4
C.) Cube root of 2
D.) Square root of 2

Answer 1

Answer:

Cube root of 4

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Answer 2

This is the cube root of 4.

Step-by-step explanation:

Here we have to apply some properties of the exponent to get the equivalent statement of the following :

We are given a mathematical expression in words which is 2 to the power 2 over 3.

The give the expression of $2^{\frac{2}{3}}$ and we have to choose from options that give the equivalent expression.

Now, $2^{\frac{2}{3}} = (2^{2}) ^{\frac{1}{3}} = 4^{\frac{1}{3}}$

{Since we know that $x^{\frac{a}{b}} = (x^{a}) ^{\frac{1}{b}} = (x^{\frac{1}{b}}) ^{a}$ from the property of exponent}

So, this is the cube root of 4. (Answer)