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Multiplicative Identity

81 / 16-3 / 4...

Question

(81/16)–¾ * [(9/25)³/² ÷ (5/2)–³]

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Solution

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{(\frac{81}{16})}^{- \frac{3}{4}} \times ⎡ ⎣ {(\frac{25}{9})}^{- \frac{3}{2}} \div {(\frac{5}{9})}^{- 3} ⎤ ⎦

(81 / 16)^{- 3 / 4} \times [(25 / 9)^{- 3 / 2} \div (5 / 2)^{- 3}]

{(\frac{81}{16})}^{\frac{- 3}{4}} \times ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ {(\frac{25}{9})}^{\frac{- 3}{2}} \div {(\frac{5}{2})}^{- 3} ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

{(\frac{81}{16})}^{- 3 / 4} \times {(\frac{25}{9})}^{- 3 / 2} \times {(\frac{2}{5})}^{- 3}

25^{\frac{3}{2}} \times 16^{- \frac{3}{4}} \times 5^{- 2} \times 1024^{\frac{3}{2}}

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