Question

Which of the following is equal to the expression below?

Answer 1

Answer:

$8\sqrt[3]{(5)}$

Step-by-step explanation:

We have been given an expression $(8\times 320)^{\frac{1}{3}$. We are asked to find which expression of given expressions is equal to our given expression.

Using exponent property $(a)^{\frac{m}{n}}=\sqrt[n]{a^m}$ we can rewrite our given expression as:

$\sqrt[3]{(8\times 320)^1}$

$\sqrt[3]{(8\times 320)}$

Rewriting 320 as $64\times 5$ in our given expression we will get,

$\sqrt[3]{(8\times 64\times 5)}$

$\sqrt[3]{(2^3\times 4^3\times 5)}$

Pulling our 2 and 4 from cube root we will get,

$2\times 4\sqrt[3]{(5)}$

$8\sqrt[3]{(5)}$

Therefore, the expression $8\sqrt[3]{(5)}$ is equal to our given expression and option D is the correct choice.

Answer 2

(8 x 320)^1/3

(2560)^1/3

(64*40)^1/3

64^1/3   *40^1/3

4 * (8^1/3) * 5^1/3

4 * 2 * 5^1/3

8 *5^1/3

None of your choices are written correctly