Question

Help its very urgent

Answer 1

`5ab^2\sqrt[3]{4a}`

Explanation:

We can simplify cube-rooted numbers as follows:

`\sqrt[3]{a^3} = a`

Because that is true, we can also say that:

`\sqrt[3]{a^4} = \sqrt[3]{a^3 \cdot a} = a\sqrt[3]{a}`

Therefore, we can simplify the given expression with the following steps:

`\sqrt[3]{500a^4b^6}`

↓ expanding the variables to put together groups of 3

`\sqrt[3]{500 \cdot a^3 \cdot a \cdot b^3 \cdot b^3}`

↓ simplifying the cube roots of the variables

`ab^2\sqrt[3]{500a}`

↓ rewriting 500 with its prime factorization

`ab^2\sqrt[3]{5^3 \cdot 2^2 \cdot a}`

↓ simplifying the cube root of
`5^3`

`\boxed{5ab^2\sqrt[3]{4a}}`