Which of the following is an equivalent expression for 5 1/2 / ^3 125 when simplified using exponent properties

Answer 1

To simplify the expression \( \frac{5 \frac{1}{2}}{(3^{125})} \), we first need to convert the mixed number \( 5 \frac{1}{2} \) into an improper fraction.

The mixed number \( 5 \frac{1}{2} \) can be converted into an improper fraction as follows:

\[ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

Now, we rewrite the given expression:

\[ \frac{5 \frac{1}{2}}{3^{125}} = \frac{\frac{11}{2}}{3^{125}} = \frac{11}{2 \cdot 3^{125}} \]

So, the simplified expression is:

\[ \frac{11}{2 \cdot 3^{125}} \]

Thus, the equivalent expression, when simplified, is \(\frac{11}{2 \cdot 3^{125}}\).

Answer 2

A. 5 ^0
B. 1/5
C. Square root 5 / 5
D. 1

Answer 3

It seems there might be a misunderstanding regarding the original expression you intended to simplify. Let's clarify the context since the options you've provided (A, B, C, D) don't directly relate to the previous mixed number and exponent expression.

If we were to consider \( 5^{\frac{1}{2}} / 3^{125} \) or any other variations of \( 5 \) and exponents, I can help clarify that.

If we are specifically looking for an equivalent expression involving \( 5 \) from the options you provided based on simplification, let’s analyze the options you listed:

1. A. \( 5^0 \): This equals 1, since any non-zero number raised to the power of zero is 1.
2. B. \( \frac{1}{5} \): This is the reciprocal of 5 and doesn't equate to \( 1 \) or \( 5^0 \).
3. C. \( \frac{\sqrt{5}}{5} \): This can be rewritten as \( 5^{1/2} \cdot 5^{-1} = 5^{1/2 - 1} = 5^{-1/2} \).
4. D. 1: This is simply a whole number.

Let's summarize:

• If you're specifically looking for an expression equivalent to \( 5^0 \): A is the correct answer, because it simplifies directly to 1.
• If you'd like an expression as the square root or extension, you could explore options C further.

If you provide the specific expression you would like to simplify, I can help further. Please clarify if you intended another expression instead of \( 5 \frac{1}{2} / 3^{125} \) or if you need to evaluate these options in a different context.