Question

Enter the factor under the radical

`(a - b) √(a - b)`
​

Answer 1

`\\ \rm\longmapsto (a-b)√(a-b)`

`\\ \rm\longmapsto (a-b)(a-b)^{(1)/(2)}`

`\\ \rm\longmapsto (a-b)^{1+(1)/(2)}`

`\\ \rm\longmapsto (a-b)^{(3)/(2)}`

Answer 2

`\dashrightarrow \: { \tt{(a - b) √(a - b) }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^(1) {(a - b)}^{ (1)/(2) } }}`

• from law of indices:

`{ \boxed{ \rm{ ({x}^(n) )( {x}^(m) ) = {x}^((n + m)) }}}`

therefore:

`\dashrightarrow \: { \tt{ {(a - b)}^{(1 + (1)/(2) )} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{ (3)/(2) } }}`