(3/5)⁴ (8/5)-¹² (32/5)6
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Posted by Swasti Parganiha 4 years, 9 months ago
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Sia ? 4 years, 9 months ago
{tex}\left(\frac{3}{5}\right)^{4}\left(\frac{8}{5}\right)^{-12}\left(\frac{32}{5}\right)^{6}{/tex} {tex}=\frac{3^{4}}{5^{4}} \times\left(\frac{5}{2^{3}}\right)^{12} \times\left(\frac{2^{5}}{5}\right)^{6}\left(\because a^{-1}=\frac{1}{a}\right){/tex}
{tex}=\frac{3^{4}}{5^{4}} \times \frac{5^{12}}{2^{36}} \times \frac{2^{30}}{5^{6}}{/tex} [ using {tex}\left(a^{m}\right)^{n}=a^{m n}{/tex} ]
{tex}=\frac{3^{4} \times 5^{12-4-6}}{2^{36-30}}{/tex} [ using {tex} \frac{a^{m}}{a^{n}}=a^{m-n}{/tex}]
{tex}=\frac{3^{4}}{2^{6}} \times 5^{2}=\frac{81 \times 25}{64}=\frac{2025}{64}{/tex}
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