Mathematics

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

2 Answer

  • 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:

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

    Step-by-step 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.

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