Answer:
A. [tex]2^7[/tex]
Step-by-step explanation:
The expression [tex]2^3 * 4^2[/tex] can be written as:
[tex]2^3 * (2*2)^2[/tex] since 4 is the product of 2².
This can be simplified into:
[tex]2^3 * (2^2)^2[/tex], which can be simplified according to the law of exponents that states: Whenever you have an exponent expression that is raised to a power, you can simplify by multiplying the outer power on the inner power:
[tex](x^m)^n = x^m^n[/tex]
This allows us to simplify the expression into:
[tex]2^3 * 2^4[/tex], which we can simplify further using the exponent property that allows us to add exponents when 2 numbers with the same base are multiplied:
[tex]2^3^+^4[/tex] = [tex]2^7[/tex]
