Which of the following is an equivalent expression for 5 1/2 / exponent 3 root 125

Question

GPT-4o mini · Answer

To simplify the expression $ \frac{5 \frac{1}{2}}{\sqrt[3]{125}} $, we first convert $ 5 \frac{1}{2} $ into an improper fraction. 1. Convert $ 5 \frac{1}{2} $: $$ 5 \frac{1}{2} = \frac{5 \cdot 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} $$ 2. Now evaluate $ \sqrt[3]{125} $: $$ \sqrt[3]{125} = 5 \quad (\text{since } 5^3 = 125) $$ 3. Now substitute these values back into the expression: $$ \frac{5 \frac{1}{2}}{\sqrt[3]{125}} = \frac{\frac{11}{2}}{5} $$ 4. To divide by a number, you multiply by the reciprocal: $$ \frac{\frac{11}{2}}{5} = \frac{11}{2} \times \frac{1}{5} = \frac{11}{10} $$ So, $ \frac{5 \frac{1}{2}}{\sqrt[3]{125}} = \frac{11}{10} $. Thus, the equivalent expression for $ 5 \frac{1}{2} / \sqrt[3]{125} $ is: $$ \frac{11}{10} $$

Messmer · Answer

The only answers given are 1/5 1 5 exponent 0 Or root 5 over 5

GPT-4o mini · Answer

Let's analyze the options given in relation to the initial expression $ \frac{5 \frac{1}{2}}{\sqrt[3]{125}} $ or $ \frac{11}{10} $.

Option 1: $ \frac{1}{5} $
Option 2: $ 1 $
Option 3: $ 5^0 $
Option 4: $ \frac{\sqrt{5}}{5} $

Now, let's evaluate the values of these options:

Option 1: $ \frac{1}{5} = 0.2 $
Option 2: $ 1 = 1 $
Option 3: $ 5^0 = 1 $
Option 4: $ \frac{\sqrt{5}}{5} = \frac{\sqrt{5}}{5} $, which can be approximated as $ \approx 0.447 $

Next, let's compare with the result obtained for $ \frac{11}{10} $: \[ \frac{11}{10} = 1.1 \]

Now, let's analyze if any of the provided answers could simplify to be equivalent to $ \frac{11}{10} $:

Comparing:
- $ \frac{1}{5} $ is not equivalent to $ \frac{11}{10} $.
- $ 1 $ is not equivalent to $ \frac{11}{10} $.
- $ 5^0 = 1 $, which is also not equivalent.
- $ \frac{\sqrt{5}}{5} \approx 0.447 $ also does not equal $ 1.1 $.

None of the options provided match $ \frac{11}{10} $.

However, let’s simplify and compare the results more closely:

If the goal is to express $ \frac{5 \frac{1}{2}}{5} $ simplistically, then: \[ 5 \frac{1}{2} = \frac{11}{2} \] \[ \frac{11/2}{5} = \frac{11}{10} \]

Now, considering the original question again, we might have made an error in interpreting $ \sqrt[3]{125} $, but let’s use values for $ \frac{\sqrt{5}}{5} $ to see if we took into account all exponents.

The equivalent to $ 5^0 $ or $ 1 $ does emerge, but it turns out that if isolating $ \frac{5 \frac{1}{2}}{5} $, nothing equates directly.

Conclusion:

Based on all these checks, and referring back and revalidating against choices provided, the simplification or original choice among provided appears limited. The closest approvable value regarding zero can point to option $1$ or $5^0$.

Thus, those two options regard highly worth in explaining $ \frac{11}{10} $, hence preferable in questioning relative $ 1 $. But ultimately, point is no exact match to $ \frac{11}{10} $.

If we layer back to conditions around those values, **the most likely selected answer among provided options while interpreting against initial expression might be $ 1$ or ( 5^0. **.