Find n so that the number sentence below is true:

2^3 x 4^3 = 2^3 x 2^n = 2^9

Answer: n=6

Step-by-step explanation:

2^3 x 4^3 = 2^3 x 2^n = 2^9

(2*2*2) * (4*4*4) = (2x2x2) * 2^n = (2x2x2x2x2x2x2x2x2)

8 x 64 = 8x 2^n = 512

512 = 8x 2^n = 512

divide all through by 8 so that 2^n can stand alone

512/8 = (8x 2^n) / 8 = 512/8

64 = 2^n = 64

express 64 as a base of 2

2^6 = 2^n = 2^6

since they all have same base, cancel out the base.

therefore,

6=n=6

n = 6