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