Solve the following: $$ \frac{2\left(r^{3} ight)^{3} imes 2 r}{2\left(r^{8} x r^{-2} ight)} $$

Question

Solve the following: $$ \frac{2\left(r^{3}ight)^{3} 	imes 2 r}{2\left(r^{8} x r^{-2}ight)} $$

UpStudy AI · Accepted Answer

1. **Simplify $$\left(r^3\right)^3$$:**

$$
   \left(r^3\right)^3 = r^{3 \times 3} = r^9
   $$

2. **Simplify the numerator:**

The numerator is:

$$
   2\left(r^3\right)^3 \times 2r = 2r^9 \times 2r = 4r^{9+1} = 4r^{10}
   $$

3. **Simplify the denominator:**

The denominator is:

$$
   2\left(r^8 \times r^{-2}\right)
   $$

First, combine the powers of $$r$$:

$$
   r^8 \times r^{-2} = r^{8-2} = r^6
   $$

Hence, the denominator becomes:

$$
   2r^6
   $$

4. **Combine the simplified numerator and denominator:**

$$
   \frac{4r^{10}}{2r^6} = \frac{4}{2} \times \frac{r^{10}}{r^6} = 2r^{10-6} = 2r^4
   $$

5. **Final Answer:**

$$
   2r^4
   $$
The simplified expression is $$2r^4$$.

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