Question

Which of the following best defines 2 2/3?

Answer 1

Answer:

A. $\sqrt[3]{4}$ = Cube root of 4.

Step-by-step explanation:

We have been given an expression $2^{\frac{2}{3}}$. We are asked to find the equivalent expression for our given expression.

Using exponent property $\sqrt[n]{a^m} =a^{\frac{m}{n}$, we will get,

$2^{\frac{2}{3}}=\sqrt[3]{2^2}$

$2^{\frac{2}{3}}=\sqrt[3]{4}$

Upon looking at our given choices, we can see that option A is the correct choice.

Answer 2

Answer:

Option A.

Step-by-step explanation:

The given expression is

$2^{\frac{2}{3}}$

We need to find the equivalent expression of given expression.

Using the properties of exponent the given expression can we written as

$(2^2)^{\frac{1}{3}}$              $[\because (a^m)^n=a^{mn}]$

$4^{\frac{1}{3}}$

Using the another property of exponent we get

$\sqrt[3]{4}$                 $[\because a^{\frac{1}{n}}=\sqrt[n]{a}]$

The expression cube root 4 is equivalent to the given expression.

Therefore, the correct option is A.