Question

If ( 5/9 )^−5 × ( 9/5 )^4 = ( 5/9 )^4n−13 , the find the value of n.​

Answer 1

$\bf\Large{Solution :}$

= (5/9)^-5×(9/5)^4=(5/9)^4n-13

= (5/9)^-5×(5/9)^-4=(5/9)^4n-13

= (5/9)^-9=(5/9)^4n-13

= Cancelling bases

= -9=4n-13

= -9+13=4n

= 4 = 4n

= n=4/4

= n=1

_____________.

Answer 2

Answer:

value of n = 1

Step-by-step explanation:

given that

$[(5/9)^-5][(9/5)^4] = (5/9)^(4n-13)$

$[(9/5)^5][(9/5)^4] = (5/9)^(4n-13)\\(9/5)^(5+4) = (5/9)^(4n-13)\\(9/5)^9 = (9/5)^(13-4n)$

bases are equal , so powers are also equal

9 = 13 - 4n

4n = 13 - 9

4n = 4

n = 1