Multiply $$ \sqrt[4]{6} \cdot \sqrt[3]{6^{2}} $$ using fractional exponents.

Question

UpStudy AI · Accepted Answer

To multiply $$ \sqrt[4]{6} \cdot \sqrt[3]{6^{2}} $$ using fractional exponents, follow these steps:

1. **Express each radical as a fractional exponent:**

$$
   \sqrt[4]{6} = 6^{1/4}
   $$
   
   $$
   \sqrt[3]{6^2} = (6^2)^{1/3} = 6^{2/3}
   $$

2. **Multiply the expressions using the properties of exponents:**

$$
   6^{1/4} \cdot 6^{2/3} = 6^{1/4 + 2/3}
   $$

3. **Add the exponents:**

To add $$ \frac{1}{4} $$ and $$ \frac{2}{3} $$, find a common denominator (which is 12):

$$
   \frac{1}{4} = \frac{3}{12}
   $$
   
   $$
   \frac{2}{3} = \frac{8}{12}
   $$
   
   $$
   \frac{3}{12} + \frac{8}{12} = \frac{11}{12}
   $$

4. **Combine the results:**

$$
   6^{1/4 + 2/3} = 6^{11/12}
   $$

**Final Answer:**

$$
6^{\,\frac{11}{12}}
$$
$$ 6^{\frac{11}{12}} $$

Multiply using fractional exponents.