Express $$ 192^{\frac{1}{5}} $$ in simplest radical form.

Question

UpStudy AI · Accepted Answer

To express $$ 192^{\frac{1}{5}} $$ in its simplest radical form, follow these steps:

1. **Factorize 192:**
   $$
   192 = 64 \times 3 = 2^6 \times 3
   $$

2. **Apply the exponent:**
   $$
   192^{\frac{1}{5}} = (2^6 \times 3)^{\frac{1}{5}} = 2^{\frac{6}{5}} \times 3^{\frac{1}{5}}
   $$

3. **Simplify the expression:**
   $$
   2^{\frac{6}{5}} = 2^{1 + \frac{1}{5}} = 2 \times 2^{\frac{1}{5}}
   $$
   Therefore:
   $$
   192^{\frac{1}{5}} = 2 \times 2^{\frac{1}{5}} \times 3^{\frac{1}{5}} = 2 \times (2 \times 3)^{\frac{1}{5}} = 2 \times 6^{\frac{1}{5}}
   $$
   
4. **Express in radical form:**
   $$
   6^{\frac{1}{5}} = \sqrt[5]{6}
   $$
   So:
   $$
   192^{\frac{1}{5}} = 2 \sqrt[5]{6}
   $$

**Final Answer:**
$$
192^{\frac{1}{5}} = 2\,\sqrt[5]{6}
$$
$$ 192^{\frac{1}{5}} = 2\,\sqrt[5]{6} $$

Express in simplest radical form.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Pre Algebra Questions