Question

Simplify
1) (11)^1/2 / (11)^1/4
2) 125^-1/3

Answer 1

Identities used :

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ {(a)}^{ - m} = ( \frac{1}{a} ) ^{m}$


1)
$\frac{ {(11)}^{ \frac{1}{2} } }{ {(11)}^{ \frac{1}{4} } } \\ \\ = {(11)}^{ \frac{1}{2} - \frac{1}{4} } \\ \\ = {11}^{ \frac{2 - 1}{4} } \\ \\ = {11}^{ \frac{1}{4} }$

2)

${(125)}^{ - \frac{1}{3} } \\ \\ = \frac{1}{ {125}^{ \frac{1}{3} } } \\ \\ = \frac{1}{ {5}^{3 \times \frac{1}{3} } } \\ \\ = \frac{1}{5} \: \: \: or \: \: \: {5}^{ - 1}$

Answer 2

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