Question

What’s the difference please help

Answer 1

C:
`-7ab \sqrt[3]{3ab^(2) }`

Explanation:

Simplify or expand:

`2ab\sqrt[3]{192ab^(2) } - 5\sqrt[3]{81a^(4) b^(5) }`

Transform the expression:

`2ab\sqrt[3]{4^(3)*3ab^(2) }` -
`5\sqrt[3]{3^(3)*3a*ab^(3) b^(2) }`

Re-write

Multiply

Combine like terms.

Answer 2

The simplified expression, written properly with square roots, is:
`\[ -7ab \sqrt[3]{a \cdot b^2} \]`

The original expression is:

`\[ 2ab \sqrt[3]{192a \cdot b^2} - 5 \sqrt[3]{81a^4 \cdot b^5} \]`

Now, rewrite the expressions inside the cube roots using prime factorization:

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

Evaluate the cube roots:

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

Evaluate the products:

`\[ 8ab \sqrt[3]{a \cdot b^2} - 15ab \sqrt[3]{a \cdot b^2} \]`

Combine the terms:

`\[ -7ab \sqrt[3]{a \cdot b^2} \]`

Therefore, the simplified expression, written properly with square roots, is:
`\[ -7ab \sqrt[3]{a \cdot b^2} \]`