Question

2^3•4^3=2^3•2^n=2^9

find a number n so that the number sentence above is true.

Answer 1

n = 6

Explanation:

`{2}^(3). {4}^(3) = {2}^(3). {2}^(n) \\ \\ {2}^(3). {( {2}^(2)) }^(3) = {2}^(3 + n) \\ \\ {2}^(3). {2 }^(6) = {2}^(3 + n) \\ \\ {2 }^(3 + 6) = {2}^(3 + n) \\ \\ {2 }^(9) = {2}^(3 + n) \\ \\ 9 = 3 + n \\ (bases \: are \: same \: so \: exponents \: will \: \\ also \: be \: equal) \\ 9 - 3 = n \\ \huge \red{ \boxed{n = 6}}`