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

3 answers

To simplify the expression \(\frac{x}{x\frac{3}{4}}\), you can start by rewriting it:

\[ \frac{x}{x \cdot \frac{3}{4}} \]

Next, you can simplify this expression. Notice that the \(x\) in the numerator and the \(x\) in the denominator can be canceled (assuming \(x \neq 0\)):

\[ = \frac{1}{\frac{3}{4}} \]

To simplify \(\frac{1}{\frac{3}{4}}\), you can multiply by the reciprocal of \(\frac{3}{4}\):

\[ = 1 \cdot \frac{4}{3} = \frac{4}{3} \]

Therefore, the expression \(\frac{x}{x\frac{3}{4}}\) simplifies to:

\[ \frac{4}{3} \]

So, the final equivalent expression is:

\[ \frac{4}{3} \]

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 \(\frac{x}{x \cdot \frac{3}{4}}\) step by step.

  1. Start with the original expression:

\[ \frac{x}{x \cdot \frac{3}{4}} \]

  1. Cancel the \(x\) in the numerator and denominator (assuming \(x \neq 0\)):

\[ = \frac{1}{\frac{3}{4}} \]

  1. Multiply by the reciprocal:

\[ = \frac{4}{3} \]

Now, it looks like we reached \(\frac{4}{3}\), but let's actually evaluate the options that have been given (a, b, c, d) to see if one of them is equivalent to \(\frac{4}{3}\).

Options Given:

a. \(x^4\)
b. \(x\)
c. \(\frac{1}{\sqrt[4]{x}}\)
d. \(\sqrt[4]{x}\)

None of these options directly simplify to \(\frac{4}{3}\). Let's try to relate them back to the original \(x\) and exponents.

From the properties of exponents:

  • \(x^{4}\) is a degree higher than \(x\)
  • \(x\) is simply itself
  • \(\frac{1}{\sqrt[4]{x}} = x^{-1/4}\)
  • \(\sqrt[4]{x} = x^{1/4}\)

None of the expressions provided can be made to equal \(\frac{4}{3}\) since they are not numerical values.

Please check the original expression. If instead of \(\frac{x}{x\frac{3}{4}}\), 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 \(\frac{x}{x\frac{3}{4}}\) resulting in a numerical value \(\frac{4}{3}\). They are all about \(x\), while we end with a constant value.

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

Similar Questions
    1. answers icon 1 answer
  1. Which expression is equivalent to `\left(x^{\frac{3}{7}}\right)^{2}`Answer choices: x^{\frac{5}{7}}, x^{\frac{6}{14}},
    1. answers icon 1 answer
    1. answers icon 1 answer
    1. answers icon 1 answer
more similar questions