How do I simplify e^(3ln2)

Question

anonymous · Answer

e^(-3ln2) 

Since there are no variables in the expression, the domain is all real numbers. 
All real numbers. 

Simplify -3ln2 by moving all terms inside the logarithm. The third law of logarithms states that the logarithm of a power of x is equal to the exponent of that power times the logarithm of x (e.g. log^b(x^(n))=nlog^b(x)). 
e^(ln(2^(-3))) 

Remove the negative exponent by rewriting 2^(-3) as (1)/(2^(3)). A negative exponent follows the rule a^(-n)=(1)/(a^(n)). 
e^(ln((1)/(2^(3)))) 

Cubing a number is the same as multiplying the number by itself 3 times (2*2*2). In this case, 2 cubed is 8. 
e^(ln((1)/(8))) 

When the base of a logarithm in the exponent and the base of the exponent are the same, the result is the argument of the logarithm. 
(1)/(8) 

The domain of the rational expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. 
All real numbers

kc_kennylau · Answer

From where did the negative sign emerge? :O