Divide $$ \frac{\sqrt[3]{7^{2}}}{\sqrt{7}} $$ using fractional expone

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UpStudy AI · Accepted Answer

To simplify the expression $$\frac{\sqrt[3]{7^{2}}}{\sqrt{7}}$$ using fractional exponents, follow these steps:

1. **Express the roots as exponents:**
   - The cube root of $$7^2$$ is $$7^{2/3}$$.
   - The square root of $$7$$ is $$7^{1/2}$$.

So, the expression becomes:
   $$
   \frac{7^{2/3}}{7^{1/2}}
   $$

2. **Subtract the exponents (since you're dividing like bases):**
   $$
   7^{2/3 - 1/2}
   $$

3. **Find a common denominator to subtract the fractions:**
   - The least common denominator of 3 and 2 is 6.
   - Convert the exponents:
     $$
     2/3 = 4/6 \quad \text{and} \quad 1/2 = 3/6
     $$
   - Subtract:
     $$
     4/6 - 3/6 = 1/6
     $$

4. **Write the simplified expression:**
   $$
   7^{1/6}
   $$

**Final Answer:**
$$
7^{\,1/6}
$$
The simplified form of the expression is $$7^{1/6}$$.

Divide using fractional expone

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