3. Write the following ratio in a simplified form: $$ 4: 4_{2}^{\frac{1}{2}} $$ A $$ 1: \frac{1}{2} $$ B. $$ 1: 1 \frac{1}{2} $$ C. $$ 1: 2 $$ D. $$ 8: 9 $$

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UpStudy AI · Accepted Answer

We start with the ratio
$$
4: 4_{2}^{\frac{1}{2}}.
$$
The notation $$4_{2}^{\frac{1}{2}}$$ denotes the square root of 4 since the index 2 indicates a square root, i.e.,
$$
4_{2}^{\frac{1}{2}} = \sqrt{4} = 2.
$$

Now the ratio becomes
$$
4: 2.
$$

To simplify, we divide both terms by their greatest common divisor, in this case 4:
$$
\frac{4}{4} : \frac{2}{4} = 1: \frac{1}{2}.
$$

Thus, the simplified form of the ratio is 
$$
1: \frac{1}{2}.
$$

The correct answer is A.
The simplified ratio is $$1: \frac{1}{2}$$, which is option A.

3. Write the following ratio in a simplified form: \[ 4: 4_{2}^{\frac{1}{2}} \] A \( 1: \frac{1}{2} \) B. \( 1: 1 \frac{1}{2} \) C. \( 1: 2 \) D. \( 8: 9 \)

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