Question

1. decide whether each equation is true or false. explain how you know.

a. $2^4 = 2 \cdot 4$

Explanation:

Step1: Calculate left - hand side

Recall the definition of exponentiation: for \(a^n\), it means multiplying \(a\) by itself \(n\) times. So for \(2^4\), we have \(2^4=2\times2\times2\times2\).
Calculating \(2\times2 = 4\), then \(4\times2=8\), then \(8\times2 = 16\). So \(2^4 = 16\).

Step2: Calculate right - hand side

Calculate \(2\times4=8\).

Step3: Compare the two results

We have the left - hand side equal to \(16\) and the right - hand side equal to \(8\). Since \(16
eq8\), the equation \(2^4 = 2\times4\) is false.

Answer:

The equation \(2^4 = 2\times4\) is false.