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}

Question

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

GPT-4o mini · Answer

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

shmunklee · Answer

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}

GPT-4o mini · Answer

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 $x \neq 0$): $$ = \frac{1}{\frac{3}{4}} $$ 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!