If 48^8 = 12^8 x 16^a then what would be the value of a?

Question

If

a+b=8,
a+c=13,
b+d=8,
c-d=6

Then

a, b, c, d  = ??

Answer 1

a= 4
(12X4)^8 = 12^8 X 4^8

4^(2x4) = 16^4

Answer 2

48 ^ 8= 12 ^ 8 * 16 ^ 9
( 2* 2* 2*2*3) ^ 8=(2*2*3) ^8 *(2*2*2*2)^a
(2^ 4 *3) ^ 8=(2^ 2*3) ^ 8 *( 2^4) ^ a
2^(4*8) * 3^ 8= 2^(2*8) * 3 ^ 8 * 2 ^(4*a)
2^32 * 3^8 =2 ^ 16 * 3 ^ 8* 2^(4a)
2 ^32 =2^(16 + 4a)
on camparing, 32=16+4a
4a=32-16
4a=16

a=4

Answer 3

we have
48^8 = 12^8 * 16^a
(12*4)^8 = 12^8 * 16^a
12^8 * 4^8 = 12^8 * 16^a
12^8 * 16^4 = 12^8 * 16^a

so, a=4

Comments

We have 48^8 = 12^8 x 16^a
So we can conclude that 48, 12, and 16 have same factor, that is 4 so :
We can change 48^8 into (4^2 x 3)^8
And then 12^8 into (4 x 3)^8 and then 16^a into (4^2)a . do u understand till this step?
Okay lets gowwww :
So,
(4^2 x 3)^8 = (4 x 3)^8 x (4^2)a
4^16 x 3^8 = 4^8 x 3^8 x 4^2a
You can move that to the same number, like this :
4^16 / 4^8 = 3^8 / 3/8 x 4^2a
U have to remember that a^m/a^n = a^m-n, and a^m . a^n = a^m+n, so :
4^16 / 4^8 = 3^8 / 3/8 x 4^2a
4^8 = 4^2a
And the you can pick the degree
8 = 2a
4 = a. Finishhh!!!! ;)))