Question

find the value of (25^3n+3 - 125^2n+3 / 125^n+1 × 5^n+1 × 25^n+1)​

Answer 1

Answer:

relation between m and n is m-n = 1.

Step-by-step explanation:

Question

find the value of (25^3n+3 - 125^2n+3 / 125^n+1 × 5^n+1 × 25^n+1)

Solution :

We can rewrite it as:

((5^2)^nx 5^(n+1) - (5^3)^n) /

((5^3)^m x 4) =1/5^3

(5^2n x 5^(n+1) - 5^3n) / (5^3m x

4) = 5^-3

(5^3n x 5 - 5^3n) / (5^3m x 4) =

(5^3n × (5-1) ) / (5^3m x 4) =

5^-3

5^-3

(5^3n x 4 ) / (5^3m x 4) = 5^-3 (5^3n/ 5^3m) = 5^-3

(5^(3n-3m)) = 5^-3

As now the base is same, i.e. 5, so equating the powers, we get:

3n-3m = -3

3m - 3n = 3

m-n=1

Answer:

So the relation between m and n is m-n = 1.

Answer 2

Answer:

5

n

×25

n−1

÷(5

n−1

×25

n−1

)

It can be written as

=5n×25

n−1

×

(5

n−1

×25

n−1

)

1

By further calculation

=5

n

×

5

n−1

1

So we get

=5

n–n+1

=5

1