Question

What is the following difference?

2 a b (RootIndex 3 StartRoot 192 a b squared EndRoot) minus 5 (RootIndex 3 StartRoot 81 a Superscript 4 Baseline b Superscript 5 Baseline EndRoot)
Negative 3 a b (RootIndex 3 StartRoot 3 a b squared EndRoot)
16 a b squared (RootIndex 3 StartRoot 3 a EndRoot) minus 45 a squared b squared (RootIndex 3 StartRoot 3 b EndRoot)
Negative 7 a b (RootIndex 3 StartRoot 3 a b squared EndRoot)
8 a b (RootIndex 3 StartRoot 3 a b squared EndRoot) minus 15 a b squared (RootIndex 3 StartRoot 3 a b EndRoot)

Answer 1

C) Negative 7 a b (RootIndex 3 StartRoot 3 a b squared EndRoot)

Explanation:

Answer 2

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

Explanation:

Remove perfect cubes from under the radical and combine like terms.

`2ab\sqrt[3]{192ab^2}-5\sqrt[3]{81a^4b^5}=2ab\sqrt[3]{4^3\cdot 3ab^2}-5\sqrt[3]{(3ab)^3\cdot 3ab^2}\\\\=(8ab -15ab)\sqrt[3]{3ab^2}=\boxed{-7ab\sqrt[3]{3ab^2} }`