Question

7²n+⁴×7⁴=(7⁸)², find n​

Answer 1

Answer:

Value of n is 4.

Step-by-step explanation:

7^( 2n + 4 ) × 7⁴ = ( 7^8 )²

7^( 2n + 4 + 4 ) = ( 7^8 )²

Since a^m × a^n = a^( m + n)

7^( 2n + 8 ) = 7^( 8 × 2 )

Since ( a^m )^n = a^( mn)

7^( 2n + 8 ) = 7^( 16 )

If bases are equal their powers also will be equal

2n + 8 = 16

2n = 16 - 8

2n = 8

n = 8/2 = 4

Therefore the value of n is 4.