Question

evaluate the following question

$( \frac{3125}{243} )^ \frac { - 4}{5}$

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

Answer 1

Answer:

1) $\frac{81}{625}$

2) $\frac{8}{27}$

Step-by-step explanation:

Given :

To evaluate the following :

1)    $( \frac{3125}{243} )^ \frac { - 4}{5}$

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

​Solution :

1)    $( \frac{3125}{243} )^ \frac { - 4}{5}$

⇒ $( \frac{5^5}{3^5} )^ \frac { - 4}{5}$

⇒$(\frac{5}{3})^{5(\frac { - 4}{5})}$

⇒$(\frac{5}{3})^{-4}$

⇒$(\frac{3}{5})^{4}$

⇒$(\frac{3^4}{5^4})$

⇒$(\frac{81}{625})$

⇒ $( \frac{3125}{243} )^ \frac { - 4}{5}$ = $(\frac{81}{625})$

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

⇒ $( \frac{3^4}{2^4} )^ \frac{ - 3}{4} \times( ( \frac{3^2}{5^2})^ \frac{3}{2} \div (\frac{5}{2})^{ - 3} )$

⇒$( \frac{3}{2} )^{4(\frac{ - 3}{4}) }\times( ( \frac{3}{5})^{2(\frac{3}{2})} \div (\frac{2}{5})^{ 3} )$

⇒ $( \frac{3}{2} )^{ - 3}\times( ( \frac{3}{5})^{3}} \div (\frac{2}{5})^{ 3} )$

⇒ $( \frac{2}{3} )^{3}\times( ( \frac{3}{5})^{3}} \times (\frac{5}{2})^{ 3} )$

⇒ $( \frac{2^3}{3^3} )\times( ( \frac{3^3}{5^3})} \times (\frac{5^3}{2^3}))$

⇒ 1

⇒ $( \frac{81}{16} )^ \frac{ - 3}{4} \times( ( \frac{9}{25})^ \frac{3}{2} \div (\frac{5}{2})^{ - 3} ) =1$