Jika a =16,b=9, dan c=81, nilai dari ab^3/2 c ^-1/3 / a^-1/2 bc^-5/6 adalah.
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Penjelasan dengan langkah-langkah:
[tex]a = 16 \\ b = 9 \\ c = 81 \\ \\ \frac{a {b}^{ \frac{3}{2} } {c}^{ - \frac{1}{3} } }{ {a}^{ - \frac{1}{2} }b {c}^{ - \frac{5}{6} } } \\ = {a}^{1 - ( - \frac{1}{2} )} {b}^{ \frac{3}{2} - 1 } {c}^{ - \frac{1}{3} - ( - \frac{5}{6}) } \\ = {a}^{ \frac{3}{2} } {b}^{ \frac{1}{2} } {c}^{ - \frac{2}{6} + \frac{5}{6} } \\ = {a}^{ \frac{3}{2} } {b}^{ \frac{1}{2} } {c}^{ \frac{1}{2} } \\ = \sqrt{ {a}^{3} } \sqrt{b} \sqrt{c} \\ = \sqrt{ {16}^{3} } \sqrt{9} \sqrt{81} \\ = \sqrt{ { ({2}^{4}) }^{3} } (3)(9) \\ = \sqrt{ {2}^{12} } (27) \\ = {2}^{6} (27) \\ = (64)(27) \\ = 1728 [/tex]
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