Bantu jawab soal itu

Bantu jawab soal itu

Sifat-sifat perpangkatan:

$boxed{begin{array}{c}{rm {a}^{m}times{a}^{n}={a}^{m+n}}\rm {a}^{m}div{a}^{n}={a}^{m-n}\rm {({a}^{m})}^{n}={a}^{mtimes n}\rm {a}^{frac{m}{n}}=sqrt[n]{{a}^{m}}\rm {a}^{-m}=frac{1}{{a}^{m}}\rm {(frac{a}{b})}^{-m}={(frac{b}{a})}^{m}\rm {(frac{a}{b})}^{m}=frac{{a}^{m}}{{b}^{m}}end{array}}$

Jawaban:

${( frac{ {a}^{ frac{2}{3} } }{ {b}^{ frac{1}{2} } }) }^{ - 1} times {( {a}^{ frac{2}{3} } {b}^{ frac{1}{2} } )}^{2} div frac{ {b}^{ frac{1}{2} } }{ {a}^{ frac{1}{3} } } \ = frac{ {a}^{ frac{2}{3} times ( - 1)} }{ {b}^{ frac{1}{2} times ( - 1) } } times {a}^{ frac{2}{3} times 2} {b}^{ frac{1}{2} times 2} times frac{ {a}^{ frac{1}{3} } }{ {b}^{ frac{1}{2} } } \ = frac{ {a}^{ - frac{2}{3} } }{ {b}^{ - frac{1}{2} } } times {a}^{ frac{4}{3} } b times frac{ {a}^{ frac{1}{3} } }{ {b}^{ frac{1}{2} } } \ = frac{ {a}^{ - frac{2}{3} } }{ {b}^{ - frac{1}{2} } } times frac{ {a}^{ frac{4}{3} } }{ {b}^{ - 1} } times frac{ {a}^{ frac{1}{3} } }{ {b}^{ frac{1}{2} } } \ = frac{ {a}^{ - frac{2}{3} + frac{4}{3} + frac{1}{3} } }{ {b}^{ - frac{1}{2} + ( - 1) + frac{1}{2} } } = frac{ {a}^{ frac{3}{3} } }{ {b}^{ - frac{2}{2} } } = frac{a}{ {b}^{ - 1} } = ab$

Jawaban: ab

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