Question

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

A. 0.25^3/2
B. 0.25 ^-3/2
C. 3/~16
D. (3/~4)^2

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

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

Explanation:

We are given the following expression:

`4^{(2)/(3)}`

Applying properties of exponents and base:

`(a^x)^y = a^(xy)\\a^(-x)= ((1)/(a))^x\\`

A. Using the exponential property
`a^(-x)= ((1)/(a))^x\\`, we can write:

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

which is not equal to the given expression.

B. Using the exponential property
`a^(-x)= ((1)/(a))^x\\`, we can write:

`(0.25)^{(-3)/(2)} = ((1)/(0.25))^{(3)/(2)} = (4)^{(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√(16) = (16)^{(1)/(3)} = (4^2)^{(1)/(3)} = 4^{(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√(4))^2 = (4^{(1)/(3)})^2 = 4^{(2)/(3)}`

which is equal to the given expression.

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