Let u=7^x. Using the rules for powers show that i) 7^x-1 = u÷7

Question

and ii) 7^2x-1 = u^2÷7

Answer 1

a ^ ( n - m ) = a ^ n / a ^ m

7 ^ ( x - 1 ) =

7 ^ x / 7 ^ 1 =

7 ^ x / 7

7 ^ x = u

so

7 ^ x / 7 = u / 7

( a ^ m ) ^ n = a ^ ( m * n )

7 ^ 2 x = ( 7 ^ x ) ^ 2

Again:

a ^ ( n - m ) = a ^ n / a ^ m

so

7 ^ ( 2 x - 1 ) =

7 ^ 2 x / 7 ^ 1 =

7 ^ 2 x / 7 =

( 7 ^ x ) ^ 2 / 7 =

u ^ 2 / 7