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?
"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.
"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.