Is $4^{x+6}-3$ an algebraic expression? $$4^{x+6}-3$$
Can we say this is an algebraic expression? I believe it is an exponential expression, but is it also an algebraic expression?
 A: "In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)." [Wikipedia: Algebraic expression]
According to this definition, $4^{x+6}-3$ is not an algebraic expression - because the integer constants ($3,4,6$) and the variables ($x$) are connected in the expression with help of non-algebraic operations. $()^x$ is not an algebraic operation, because transcendental (= non-algebraic) operations are needed, e.g.: $a^x=e^{x\ln(a)}$. 
But a completely different question is, if the value of the expression is algebraic (an algebraic number) or not.
An exponential expression is a mathematical expression that contains an exponent that is a non-rational expression of the considered variables.
According to this definition, $4^{x+6}-3$ is an exponential expression.
Remember that exponentiation by an exponent that is a rational number is an algebraic operation, but exponentiation by an exponent that is not a rational number is a non-algebraic operation.
