Question

$${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8$$  is equal to

पर्याय

• $${(-\frac{1}{5})}^5$$

   

• $${(-\frac{1}{5})}^{11}$$

   

• $$(-5{)}^5$$

   

• $${\left(\frac{1}{5}\right)}^5$$

   

Answer 1

$$(-5{)}^5$$
We have:
$${\left(\frac{-1}{5}\right)}^3÷{\left(\frac{-1}{5}\right)}^8$$ ${\displaystyle ={\left(\frac{-1}{5}\right)}^{3-8}}$

${\displaystyle ={\left(\frac{-1}{5}\right)}^{-5}}$

${\displaystyle =\frac{1}{{\left(\frac{-1}{5}\right)}^5}}$

${\displaystyle =\frac{1}{\left(\frac{{(-1)}^5}{5^5}\right)}}$

${\displaystyle =\frac{5^5}{{(-1)}^5}}$

${\displaystyle ={\left(\frac{5}{-1}\right)}^5}$

${\displaystyle ={(-5)}^5}$