using the properties of exponents, which expression is equivalent to \frac{x}{x\frac{3}{4}}

3 answers

To simplify the expression xx34, you can start by rewriting it:

xx34

Next, you can simplify this expression. Notice that the x in the numerator and the x in the denominator can be canceled (assuming x0):

=134

To simplify 134, you can multiply by the reciprocal of 34:

=143=43

Therefore, the expression xx34 simplifies to:

43

So, the final equivalent expression is:

43

using the properties of exponents, which expression is equivalent to \frac{x}{x\frac{3}{4}}
a. x^4
b. x
c. \frac{1}{\sqrt[4]{x}}
d. \sqrt[4]{x}

Let's simplify the expression xx34 step by step.

  1. Start with the original expression:

xx34

  1. Cancel the x in the numerator and denominator (assuming x0):

=134

  1. Multiply by the reciprocal:

=43

Now, it looks like we reached 43, but let's actually evaluate the options that have been given (a, b, c, d) to see if one of them is equivalent to 43.

Options Given:

a. x4
b. x
c. 1x4
d. x4

None of these options directly simplify to 43. Let's try to relate them back to the original x and exponents.

From the properties of exponents:

  • x4 is a degree higher than x
  • x is simply itself
  • 1x4=x1/4
  • x4=x1/4

None of the expressions provided can be made to equal 43 since they are not numerical values.

Please check the original expression. If instead of xx34, it was intended to present a different expression involving x where exponent terms would cancel, let me know so I can assist further. As it stands now, none of the options a, b, c, or d correspond to xx34 resulting in a numerical value 43. They are all about x, while we end with a constant value.

If something else was intended with the options provided, please clarify!

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