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

Answer 1

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 $x\ne 0$):

$$=\frac{1}{\frac{3}{4}}$$

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:

$$\frac{4}{3}$$

Answer 2

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}

Answer 3

Let's simplify the expression $\frac{x}{x\cdot \frac{3}{4}}$ step by step.

1. Start with the original expression:

$$\frac{x}{x\cdot \frac{3}{4}}$$

2. Cancel the $x$ in the numerator and denominator (assuming $x\ne 0$):

$$=\frac{1}{\frac{3}{4}}$$

3. 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!