Divide these numbers using fractional exponents. $$ \frac{\sqrt{6^{3}}}{\sqrt[4]{6}} $$

Question

UpStudy AI · Accepted Answer

To divide the numbers using fractional exponents, let's break down the expression:

$$
\frac{\sqrt{6^{3}}}{\sqrt[4]{6}}
$$

1. **Convert the roots to fractional exponents:**
   - The square root of $$6^3$$ is:
     $$
     \sqrt{6^{3}} = (6^{3})^{1/2} = 6^{3/2}
     $$
   - The fourth root of $$6$$ is:
     $$
     \sqrt[4]{6} = 6^{1/4}
     $$

2. **Set up the division with exponents:**
   $$
   \frac{6^{3/2}}{6^{1/4}}
   $$

3. **Subtract the exponents (since the bases are the same):**
   $$
   6^{3/2 - 1/4} = 6^{6/4 - 1/4} = 6^{5/4}
   $$

So, the simplified form using fractional exponents is:

$$
6^{5/4}
$$

**Final Answer:**
$$
6^{5/4}
$$
The simplified form is $$6^{5/4}$$.

Divide these numbers using fractional exponents.

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions