Question

Exponent and powers

$simplify \: \: ( \frac{a {}^{3} \: b {}^{2} }{ab {}^{3} } ) {}^{ - 3}$
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Answer 1

ANSWER:

$\frac{b^3}{ {a}^{6} }$

GIVEN:

$( \frac{a^{3} \: b^{2} }{ab^{3} } )^{ - 3}$

TO DO:

SIMPLIFICATION OF $( \frac{a^{3} \: b^{2} }{ab^{3} } )^{ - 3}$

FORMULAE:

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

EXPLANATION:

$= { (\frac{a {b}^{3} }{ {a}^{3} {b}^{2} }) }^{3} \\ \\ = \frac{ {a}^{3} {b}^{9} }{ {a}^{9} {b}^{6}} \\ \\ = \frac{ {b}^{9 - 6} }{ {a}^{9 - 3} } \\ \\ = \frac{b^3}{ {a}^{6} }$

HENCE THE SIMPLIFIED VALUE IS $\frac{b^3}{ {a}^{6} }$