Answer :
- Calculate $16^{\frac{2}{3}}$ which is approximately 6.3496.
- Convert this value to a percentage by dividing by 100, resulting in 0.063496.
- Multiply the percentage by 186: $0.063496 \times 186 \approx 11.81026$.
- The final answer is approximately $\boxed{11.81}$.
### Explanation
1. Understanding the Problem
We need to calculate $16^{\frac{2}{3}}\%$ of 186. This means we first need to find the value of $16^{\frac{2}{3}}$, then convert it to a percentage, and finally multiply that percentage by 186.
2. Calculating 16^(2/3)
Let's calculate $16^{\frac{2}{3}}$. We can rewrite this as $(2^4)^{\frac{2}{3}} = 2^{\frac{8}{3}}$. Using a calculator, we find that $16^{\frac{2}{3}} \approx 6.3496$.
3. Converting to Percentage
Now, we need to express this value as a percentage. To do this, we divide by 100: $\frac{6.3496}{100} = 0.063496$.
4. Multiplying by 186
Finally, we multiply this percentage by 186: $0.063496 \times 186 \approx 11.81026$.
5. Final Answer
Therefore, $16^{\frac{2}{3}}\%$ of 186 is approximately 11.81.
### Examples
Understanding percentages is crucial in everyday life, from calculating discounts while shopping to determining interest on loans or investments. For instance, if a store offers a discount of $16^{\frac{2}{3}}\%$ on an item priced at $186, you would calculate the discount amount using the steps outlined above to determine how much money you'll save. This skill helps in making informed financial decisions and understanding the true cost or savings in various scenarios.
- Convert this value to a percentage by dividing by 100, resulting in 0.063496.
- Multiply the percentage by 186: $0.063496 \times 186 \approx 11.81026$.
- The final answer is approximately $\boxed{11.81}$.
### Explanation
1. Understanding the Problem
We need to calculate $16^{\frac{2}{3}}\%$ of 186. This means we first need to find the value of $16^{\frac{2}{3}}$, then convert it to a percentage, and finally multiply that percentage by 186.
2. Calculating 16^(2/3)
Let's calculate $16^{\frac{2}{3}}$. We can rewrite this as $(2^4)^{\frac{2}{3}} = 2^{\frac{8}{3}}$. Using a calculator, we find that $16^{\frac{2}{3}} \approx 6.3496$.
3. Converting to Percentage
Now, we need to express this value as a percentage. To do this, we divide by 100: $\frac{6.3496}{100} = 0.063496$.
4. Multiplying by 186
Finally, we multiply this percentage by 186: $0.063496 \times 186 \approx 11.81026$.
5. Final Answer
Therefore, $16^{\frac{2}{3}}\%$ of 186 is approximately 11.81.
### Examples
Understanding percentages is crucial in everyday life, from calculating discounts while shopping to determining interest on loans or investments. For instance, if a store offers a discount of $16^{\frac{2}{3}}\%$ on an item priced at $186, you would calculate the discount amount using the steps outlined above to determine how much money you'll save. This skill helps in making informed financial decisions and understanding the true cost or savings in various scenarios.
