To determine which expression correctly converts 80 US dollars (USD) to Australian dollars (AUD), we need to analyze the exchange rates given:
- 1 USD = 1.0343 AUD
- 1 AUD = 0.9668 USD
We are given 80 USD and we need to convert it to AUD. To do this, we need to multiply by the conversion rate from USD to AUD, which is 1.0343 AUD per 1 USD.
Among the provided options, we can eliminate the incorrect units by dimensional analysis:
1. [tex]\( 80 \text{ USD} \times \frac{0.9668 \text{ USD}}{1 \text{ AUD}} \)[/tex]
- Units result in [tex]\( \text{USD}^2 / \text{AUD} \)[/tex], which is incorrect for our conversion as it combines USD with itself instead of converting to AUD.
2. [tex]\( 80 \text{ USD} \times \frac{1.0343 \text{ USD}}{1 \text{ AUD}} \)[/tex]
- Units result in [tex]\( \text{USD}^2 / \text{AUD} \)[/tex], which is again incorrect.
3. [tex]\( 80 \text{ USD} \times \frac{0.9668 \text{ AUD}}{1 \text{ USD}} \)[/tex]
- Units result in [tex]\( \text{USD} \times \text{AUD} / \text{USD} = \text{AUD} \)[/tex]. This converts to AUD, but the value is incorrect as it uses the reverse conversion rate from AUD to USD.
4. [tex]\( 80 \text{ USD} \times \frac{1.0343 \text{ AUD}}{1 \text{ USD}} \)[/tex]
- Units result in [tex]\( \text{USD} \times \text{AUD} / \text{USD} = \text{AUD} \)[/tex]. This converts correctly to AUD using the direct conversion rate from USD to AUD.
Therefore, the correct expression to convert 80 USD to AUD is:
[tex]\[ 80 \text{ USD} \times \frac{1.0343 \text{ AUD}}{1 \text{ USD}} \][/tex]
This matches option 4. Hence, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
