Which of the following is equal to the expression below

A. 40
B.
C. 30
D.

Ask by George Herrera. in the United States

Jan 24,2025

Question

Which of the following is equal to the expression below $$ (8 \cdot 320)^{\frac{1}{3}} $$ A. 40 B. $$ 8 \sqrt[3]{5} $$ C. 30 D. $$ 10 \sqrt[3]{5} $$

UpStudy AI · Accepted Answer

To determine which option is equal to the expression $$ (8 \cdot 320)^{\frac{1}{3}} $$, let's simplify the expression step by step.

1. **Multiply the values inside the parentheses:**
   $$
   8 \cdot 320 = 2560
   $$
   
2. **Express 2560 in terms of its prime factors:**
   $$
   2560 = 2^9 \cdot 5
   $$
   
3. **Apply the cube root to the prime factorization:**
   $$
   (2^9 \cdot 5)^{\frac{1}{3}} = 2^{3} \cdot 5^{\frac{1}{3}} = 8 \cdot \sqrt[3]{5}
   $$
   
So, the simplified form of $$ (8 \cdot 320)^{\frac{1}{3}} $$ is $$ 8 \sqrt[3]{5} $$.

**Answer:**  
**B. $$ 8 \sqrt[3]{5} $$**
The answer is $$ 8 \sqrt[3]{5} $$, choice B.

Which of the following is equal to the expression below

A. 40
B.
C. 30
D.

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