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Convert the following expressions to radicals. 4. y^(12)/(4)= 5. 6^(2)/(3)= 6. 5^(2)/(5)= 7. 1^(7)/(4)= 8. 2^(1)/(3)= 9. u^(3)/(13)=

Question

Convert the following expressions to radicals. 4. y^(12)/(4)= 5. 6^(2)/(3)= 6. 5^(2)/(5)= 7. 1^(7)/(4)= 8. 2^(1)/(3)= 9. u^(3)/(13)=

Convert the following expressions to radicals.
4. y^(12)/(4)= 
5. 6^(2)/(3)= 
6. 5^(2)/(5)= 
7. 1^(7)/(4)= 
8. 2^(1)/(3)= 
9. u^(3)/(13)=

Solution

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JosieMaster · Tutor for 5 years

Answer

### 4. \( y^3 \)<br />### 5. \( \sqrt[3]{6^2} \)<br />### 6. \( \sqrt[5]{5^2} \)<br />### 7. \( 1 \)<br />### 8. \( \sqrt[3]{2} \)<br />### 9. \( \sqrt[13]{u^3} \)

Explain

## Step 1: Convert \( y^{\frac{12}{4}} \) to a radical<br />### The expression \( y^{\frac{12}{4}} \) simplifies to \( y^3 \) because \( \frac{12}{4} = 3 \). Therefore, it is not expressed as a radical but rather as a simple power.<br /><br />## Step 2: Convert \( 6^{\frac{2}{3}} \) to a radical<br />### The expression \( 6^{\frac{2}{3}} \) can be rewritten as the cube root of \( 6^2 \), which is \( \sqrt[3]{6^2} \).<br /><br />## Step 3: Convert \( 5^{\frac{2}{5}} \) to a radical<br />### The expression \( 5^{\frac{2}{5}} \) can be rewritten as the fifth root of \( 5^2 \), which is \( \sqrt[5]{5^2} \).<br /><br />## Step 4: Convert \( 1^{\frac{7}{4}} \) to a radical<br />### Since any number raised to any power is still 1, \( 1^{\frac{7}{4}} = 1 \). It does not need to be expressed as a radical.<br /><br />## Step 5: Convert \( 2^{\frac{1}{3}} \) to a radical<br />### The expression \( 2^{\frac{1}{3}} \) is the cube root of 2, which is \( \sqrt[3]{2} \).<br /><br />## Step 6: Convert \( u^{\frac{3}{13}} \) to a radical<br />### The expression \( u^{\frac{3}{13}} \) can be rewritten as the thirteenth root of \( u^3 \), which is \( \sqrt[13]{u^3} \).
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