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

1. User Answers stephbry017
Answer:It's .25 3/2
Stepbystep explanation:It's the only equation the has a flipped fraction of 3/2 instead of 2/3.

2. User Answers ChiKesselman
Answer:
Option A and Option B are not equivalent to the given expression.
Stepbystep explanation:
We are given the following expression:
[tex]4^{\frac{2}{3}}[/tex]
Applying properties of exponents and base:
[tex](a^x)^y = a^{xy}\\a^{x}= (\frac{1}{a})^x\\[/tex]
A. Using the exponential property [tex]a^{x}= (\frac{1}{a})^x\\[/tex], we can write:
[tex]0.25^{\frac{3}{2}} = (\frac{1}{0.25})^{\frac{3}{2}} = (4)^{\frac{3}{2}}[/tex]
which is not equal to the given expression.
B. Using the exponential property [tex]a^{x}= (\frac{1}{a})^x\\[/tex], we can write:
[tex](0.25)^{\frac{3}{2}} = (\frac{1}{0.25})^{\frac{3}{2}} = (4)^{\frac{3}{2}}[/tex]
which is not equal to the given expression.
C. First we convert the radical form into exponent form. Then by using the property [tex](a^x)^y = a^{xy}[/tex] of exponent, we can write the following:
[tex]^3\sqrt{16} = (16)^{\frac{1}{3}} = (4^2)^{\frac{1}{3}} = 4^{\frac{2}{3}}[/tex]
which is equal to the given expression.
D. First we convert the radical form into exponent form. Then by using the property [tex](a^x)^y = a^{xy}[/tex] of exponent, we can write the following:
[tex](^3\sqrt{4})^2 = (4^{\frac{1}{3}})^2 = 4^{\frac{2}{3}}[/tex]
which is equal to the given expression.
Option D and Option C are equivalent to the given expression.