Question

Enter the factor under the radicalula1" title="(a - b) \sqrt{a - b} " alt="(a - b) \sqrt{a - b} " align="absmiddle" class="latex-formula">
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Answer 1

$\\ \rm\longmapsto (a-b)\sqrt{a-b}$

$\\ \rm\longmapsto (a-b)(a-b)^{\frac{1}{2}}$

$\\ \rm\longmapsto (a-b)^{1+\dfrac{1}{2}}$

$\\ \rm\longmapsto (a-b)^{\dfrac{3}{2}}$

Answer 2

Answer:

$\dashrightarrow \: { \tt{(a - b) \sqrt{a - b} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{1} {(a - b)}^{ \frac{1}{2} } }}$

• from law of indices:

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

therefore:

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