Question

Which of the following is equal to the expression below?

(8 x 320)^1/3

A. 10 ^3 root 5

B. 40

C. 30

D. 8 ^3 root 5

Answer 1

(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 2

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

Explanation:

We have been given an expression
`(8* 320)^{(1)/(3)`. We are asked to find which expression of given expressions is equal to our given expression.

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

`\sqrt[3]{(8* 320)^1}`

`\sqrt[3]{(8* 320)}`

Rewriting 320 as
`64* 5` in our given expression we will get,

`\sqrt[3]{(8* 64* 5)}`

`\sqrt[3]{(2^3* 4^3* 5)}`

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

`2* 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.