Answer:
(B)[tex]2^1[/tex]
Step-by-step explanation:
We are to simplify the given expression: [tex]\dfrac{2^2 \cdot 2^3}{2^4}[/tex]
Step 1: Apply the addition law of indices to simplify the numerator.
[tex]\text{Addition Law: }a^x \cdot a^y=a^{x+y}[/tex]
Therefore:
[tex]\dfrac{2^2 \cdot 2^3}{2^4} \\\\=\dfrac{2^{2+3}}{2^4}\\\\=\dfrac{2^5}{2^4}[/tex]
Step 2: Apply the Subtraction law of indices to simplify the expression
[tex]\text{Subtraction Law: }a^x \div a^y=a^{x-y}\\\\\implies \dfrac{2^5}{2^4} =2^{5-4}\\\\=2^1[/tex]
The correct option is B.
