Question

-5^4÷-5^2=5^n ...find value of n​

Answer 1

Answer :-

• Value of n is 2

Solution :-

$\rm \: ( - 5)^{4} \div ({ - 5})^{2} = {5}^{n}$

$\rm \implies( - 5 \times - 5 \times - 5 \times - 5) \div ( - 5 \times - 5) = {5}^{n}$

$\implies \rm625 \: \div 25 = {5}^{n}$

$\implies25 \: = {5}^{2}$

So, in place of N the value came 2 because 25 is 5 square.

How we can solve this :-

There is a power of 5 given so, we will expand it and write, so it becomes -5 four times and -5 two times . And that is equal to 5 raised to the power of N . So, we will find the value of them and sign how can we manage . Let's see!!

If - is Expressed in even times

(i.e.4,6,8,10,20,30,32..etc..) then the substract sign becomes positive and if ,

- is Expressed in odd times

(i.e.3,5,7,9,13,15,19..etc..) then the substract sign remains negative.

And then simply dividing 625 and 25 and the value comes is 25 which is equal to 5 raised to square.