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Convert the following radicals to exponents.

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Convert the following radicals to exponents.

Convert the following radicals to exponents.

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CaseyMaster · Tutor for 5 years

Answer

### 10. \( 8^{\frac{4}{7}} \)<br />### 11. \( 35^{\frac{1}{3}} \)<br />### 12. \( 24^{\frac{1}{5}} \)<br />### 13. \( f^{\frac{7}{8}} \)<br />### 14. \( h^{\frac{3}{16}} \)<br />### 15. \( 9^{\frac{3}{8}} \)

Explain

## Step 1: Understanding Radical to Exponent Conversion<br />### The general rule for converting a radical expression $\sqrt[n]{a^m}$ into an exponent is to express it as $a^{\frac{m}{n}}$. This means the root becomes the denominator of the exponent, and the power inside the radical becomes the numerator.<br /><br />## Step 2: Applying the Rule to Each Problem<br /><br />### Problem 10: \( \sqrt[7]{8^4} \)<br />- Convert using the rule: \( 8^{\frac{4}{7}} \).<br /><br />### Problem 11: \( \sqrt[3]{35} \)<br />- Convert using the rule: \( 35^{\frac{1}{3}} \).<br /><br />### Problem 12: \( \sqrt[5]{24} \)<br />- Convert using the rule: \( 24^{\frac{1}{5}} \).<br /><br />### Problem 13: \( \sqrt[8]{f^7} \)<br />- Convert using the rule: \( f^{\frac{7}{8}} \).<br /><br />### Problem 14: \( \sqrt[16]{h^3} \)<br />- Convert using the rule: \( h^{\frac{3}{16}} \).<br /><br />### Problem 15: \( \sqrt[8]{9^3} \)<br />- Convert using the rule: \( 9^{\frac{3}{8}} \).
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