Question

Which option lists an expression that is not equivalent to 4 2/3?

Answer 1

Answer:It's .25 3/2

Step-by-step explanation:It's the only equation the has a flipped fraction of 3/2 instead of 2/3.

Answer 2

Answer:

Option A and Option B are not equivalent to the given expression.

Step-by-step explanation:

We are given the following expression:

$4^{\frac{2}{3}}$

Applying properties of exponents and base:

$(a^x)^y = a^{xy}\\a^{-x}= (\frac{1}{a})^x$

A. Using the exponential property $a^{-x}= (\frac{1}{a})^x$, we can write:

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

which is not equal to the given expression.

B. Using the exponential property $a^{-x}= (\frac{1}{a})^x$, we can write:

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

which is not equal to the given expression.

C. First we convert the radical form into exponent form. Then by using the property $(a^x)^y = a^{xy}$ of exponent, we can write the following:

$^3\sqrt{16} = (16)^{\frac{1}{3}} = (4^2)^{\frac{1}{3}} = 4^{\frac{2}{3}}$

which is equal to the given expression.

D. First we convert the radical form into exponent form. Then by using the property $(a^x)^y = a^{xy}$ of exponent, we can write the following:

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

which is equal to the given expression.

Option D and Option C are equivalent to the given expression.