Subjects algebra

Radical Evaluation 6902C6

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1. **State the problem:** We need to express the last row's expression in radical notation, rational exponents, and evaluate it to two decimal places. 2. **Identify the expression:** The last row is "6th root of 5^7". 3. **Write in radical notation:** This is already given as $\sqrt[6]{5^7}$. 4. **Write using rational exponents:** The 6th root of $5^7$ is written as $5^{\frac{7}{6}}$. 5. **Evaluate the expression:** Calculate $5^{\frac{7}{6}}$ using a calculator. $$5^{\frac{7}{6}} = e^{\ln(5) \times \frac{7}{6}}$$ Using approximate values: $$\ln(5) \approx 1.60944$$ $$1.60944 \times \frac{7}{6} = 1.60944 \times 1.1667 \approx 1.877$$ $$e^{1.877} \approx 6.53$$ 6. **Final answer:** - Written in radical notation: $\sqrt[6]{5^7}$ - Written using rational exponents: $5^{\frac{7}{6}}$ - Evaluated to two decimal places: 6.53 This completes the last row of the table.