Question

please can you solve it for me ​

Answer 1

(4/5) ki power -5 ÷ (16/25) ki power -2

16/25 ÷ 256/625

0.64 ÷ 0.4096

1.5625

I hope help us❤

Answer 2

Question :

By what number should $\small \tt\purple{( \frac{4}{5} )^{ - 5}}$ be divided to get $\small \tt\orange{( \frac{16}{25} ) ^{ - 2} }$ ?

What to do ?

ln this question it is asked that what number we can take so that if we will divide $\small \tt\purple{( \frac{4}{5} )^{ - 5}}$ by that number it will result to $\small \tt\orange{( \frac{16}{25} ) ^{ - 2} }$

So for finding that number we need to assume that number to be any of the alphabetical number as you wish (like x ,a ,b etc..) so after taking that we will find that assumption alphabetical number and after finding it we will able to take out that number what it was !

Now , let's solve !

Solution :

$\pmb {\tt {\colorbox{brown}{assumption : }}}$

Let consider x be the number which should divide $\small \tt\purple{( \frac{4}{5} )^{ - 5}}$ to get

$\small \tt\orange{( \frac{16}{25} ) ^{ - 2} }$ .

Now,

$\Rightarrow \bf {\color{green}x \div (\frac{4}{5} )^{ - 5} = ( \frac{16}{25} ) ^{ - 2} }$

$\Rightarrow \bf {\color{green}x \div (\frac{5}{4} )^{ 5} = ( \frac{25}{16} ) ^{ 2} }$

$\Rightarrow \bf {\color{green}x = \frac{625}{256} \times (\frac{256}{625} )^{1} }$

$\Rightarrow \bf {\color{green}x = \frac{\cancel{{625}} \: \purple{1}}{\cancel{{256}} \: \purple{1}} \times (\frac {\cancel{{256}} \: \purple{1}}{\cancel{{625}} \: \purple{1}} )^{1} }$

$\Rightarrow \bf {\color{green}x = (1) ^{1} = 1 }$

$\boxed{\bf{ \therefore \: x = 1}}$

Verification :

$\Rightarrow \bf {\color{magenta}1 \div (\frac{4}{5} )^{ - 5} = ( \frac{16}{25} ) ^{ - 2} }$

$\Rightarrow \bf {\color{magenta}1 \div (\frac{5}{4} )^{ 5} = ( \frac{25}{16} ) ^{ 2} }$

$\Rightarrow \bf {\color{magenta}1 = \frac{625}{256} \times (\frac{256}{625} )^{1} }$

$\Rightarrow \bf {\color{magenta}1 = \frac{\cancel{{625}} \: \purple{1}}{\cancel{{256}} \: \purple{1}} \times (\frac {\cancel{{256}} \: \purple{1}}{\cancel{{625}} \: \purple{1}} )^{1} }$

$\Rightarrow \bf {\color{magenta}1 = (1) ^{1} = 1 }$

$\boxed{\bf \pink{ \therefore \: 1 = 1}}$

$\tt{hence \: \: verified }$