Write the following expression in simplest form.

(Simplify yourannswer. Type an exact answer, using radicals as needed.)

Ask by Clarke Riley. in the United States

Jan 24,2025

Question

Write the following expression in simplest form. $$ \sqrt{2^{5} \cdot 13^{3}} $$ $$ \sqrt{2^{5} \cdot 13^{3}}= $$ (Simplify yourannswer. Type an exact answer, using radicals as needed.)

UpStudy AI · Accepted Answer

To simplify the expression $$ \sqrt{2^{5} \cdot 13^{3}} $$, follow these steps:

1. **Rewrite the Square Root as Exponents:**
   $$
   \sqrt{2^{5} \cdot 13^{3}} = (2^{5} \cdot 13^{3})^{\frac{1}{2}}
   $$

2. **Apply the Exponent to Each Factor:**
   $$
   = 2^{\frac{5}{2}} \cdot 13^{\frac{3}{2}}
   $$

3. **Simplify Each Term Separately:**
   - For $$ 2^{\frac{5}{2}} $$:
     $$
     2^{\frac{5}{2}} = 2^{2 + \frac{1}{2}} = 2^2 \cdot 2^{\frac{1}{2}} = 4\sqrt{2}
     $$
   
   - For $$ 13^{\frac{3}{2}} $$:
     $$
     13^{\frac{3}{2}} = 13^{1 + \frac{1}{2}} = 13 \cdot 13^{\frac{1}{2}} = 13\sqrt{13}
     $$

4. **Multiply the Simplified Terms:**
   $$
   4\sqrt{2} \cdot 13\sqrt{13} = (4 \times 13) \cdot (\sqrt{2} \times \sqrt{13}) = 52\sqrt{26}
   $$

So, the expression in its simplest form is:

$$
\sqrt{2^{5} \cdot 13^{3}} = 52\sqrt{26}
$$

**Answer:**  
$$52\,\sqrt{26}$$
$$52\sqrt{26}$$

Write the following expression in simplest form.

(Simplify yourannswer. Type an exact answer, using radicals as needed.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Pre Algebra Questions

Write the following expression in simplest form. (Simplify yourannswer. Type an exact answer, using radicals as needed.)