Question

Evaluate : (125)^ -(2/3)÷(8)^2/3​

Answer 1

ANSWER:

${ \bf{ \to \dfrac{ {125}^{ - \frac{2}{3} } }{ { 8 }^{ \frac{2}{3} } } }}$

Using

${ \rm{ {a}^{ \frac{x}{y} } = \sqrt[y]{ {a}^{x} } }}$

${ \sf{ \implies \dfrac{ \sqrt[3]{ {125}^{ - 2} } }{ \sqrt[3]{ {8}^{2} } } }}$

Using

$\rm \sqrt{ \dfrac{a}{b} } = \dfrac{ \sqrt{a} }{ \sqrt{b} }$

${ \rm{ {a}^{ - x} = \frac{1}{ {a}^{x} } }}$

${ \rm{ {( {a}^{m} )}^{n} = {( {a}^{n}) }^{m} }}$

${ \sf{ \implies \dfrac{ \sqrt[3]{ \dfrac{1}{ { ({5}^{2} })^{3} } } }{ \sqrt[3]{ ({ {2}^{2} })^{3} } } }}$

${ \sf{ \implies \dfrac{ \frac{1}{ \sqrt[ \cancel3]{ {( {5}^{2} })^ { \cancel3} } } }{ \sqrt[ \cancel3]{ { ({2}^{2}) }^{ \cancel3} } } = \dfrac{ \frac{1}{25} }{4} }}$

${ \sf { \implies \dfrac{1}{100} }}$

Hence,

125^-⅔÷8^⅔ = 1/100 = 0.01