$$ 2 \sqrt[3]{7 x^{2}} $$ and $$ 8 \sqrt[3]{6 x^{2}} $$

Question

UpStudy AI · Accepted Answer

It looks like you've provided two expressions involving cube roots:

1. $$ 2 \sqrt[3]{7x^{2}} $$
2. $$ 8 \sqrt[3]{6x^{2}} $$

Let's explore how to simplify and potentially combine these expressions.

### Simplifying Each Expression

1. **First Expression:**
   $$
   2 \sqrt[3]{7x^{2}}
   $$
   This can be rewritten using exponent notation:
   $$
   2 \cdot 7^{1/3} \cdot x^{2/3}
   $$
   So, the simplified form is:
   $$
   2 \cdot 7^{1/3} \cdot x^{2/3}
   $$

2. **Second Expression:**
   $$
   8 \sqrt[3]{6x^{2}}
   $$
   Similarly, using exponent notation:
   $$
   8 \cdot 6^{1/3} \cdot x^{2/3}
   $$
   This can also be expressed by factoring out constants:
   $$
   2^3 \cdot 6^{1/3} \cdot x^{2/3} = 2 \cdot 2^2 \cdot 6^{1/3} \cdot x^{2/3}
   $$
   Simplifying further:
   $$
   8 \cdot 6^{1/3} \cdot x^{2/3}
   $$

### Combining the Expressions

Both expressions share a common term $$ x^{2/3} $$. We can factor this out to combine the expressions:

$$
2 \cdot 7^{1/3} \cdot x^{2/3} + 8 \cdot 6^{1/3} \cdot x^{2/3} = x^{2/3} \left(2 \cdot 7^{1/3} + 8 \cdot 6^{1/3}\right)
$$

### Final Simplified Form

The combined expression is:

$$
x^{2/3} \left(2 \cdot \sqrt[3]{7} + 8 \cdot \sqrt[3]{6}\right)
$$

This is as simplified as the expression can get unless there are specific values for $$x$$ or further context provided.

### Summary

- **Simplified First Expression:** $$ 2 \cdot 7^{1/3} \cdot x^{2/3} $$
- **Simplified Second Expression:** $$ 8 \cdot 6^{1/3} \cdot x^{2/3} $$
- **Combined Expression:** $$ x^{2/3} \left(2 \cdot \sqrt[3]{7} + 8 \cdot \sqrt[3]{6}\right) $$

If you have a specific operation in mind (like adding, subtracting, multiplying, etc.) or need further assistance with these expressions, feel free to provide more details!
The expressions can be combined as $$ x^{2/3} \left(2 \cdot \sqrt[3]{7} + 8 \cdot \sqrt[3]{6}\right) $$.

and

Solución de inteligencia artificial de Upstudy

Responder

Solución

Simplifying Each Expression

Combining the Expressions

Final Simplified Form

Summary

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions