Respuesta :

wegnerkolmp2741o

(8 x 320)^(1/3)

First, multiply inside the parentheses.

(2560)^(1/3)

We want to use the property (a*b) ^c = a^c  * b^c so we need to find a perfect cube inside the parentheses and rewrite.

(64*40)^(1/3)

64^(1/3)   *40^(1/3)

We want to rewrite 40 with a perfect cube.

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

4 * 2 * 5^(1/3)

8 *5^(1/3)

None of your choices are written correctly

Answer:

[tex]8\sqrt[3]{(5)}[/tex]

Step-by-step explanation:

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

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

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

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

Rewriting 320 as [tex]64\times 5[/tex] in our given expression we will get,

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

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

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

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

[tex]8\sqrt[3]{(5)}[/tex]

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