The problem asks us to determine whether the following equations are true or false: 1. $3^5 = 3 \times 5$

1. Problem Description

The problem asks us to determine whether the following equations are true or false:

1. $3^5 = 3 \times 5$

2. $3^5 = 5^3$

3. $1^3 = 5^3$

2. Solution Steps

Let's evaluate each equation:

1. $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$ and $3 \times 5 = 15$. Since $243 \neq 15$, the equation $3^5 = 3 \times 5$ is false.

2. $3^5 = 243$ (as calculated above) and $5^3 = 5 \times 5 \times 5 = 125$. Since $243 \neq 125$, the equation $3^5 = 5^3$ is false.

3. $1^3 = 1 \times 1 \times 1 = 1$ and $5^3 = 125$ (as calculated above). Since $1 \neq 125$, the equation $1^3 = 5^3$ is false.

3. Final Answer

1. $3^5 = 3 \times 5$ is False

2. $3^5 = 5^3$ is False

3. $1^3 = 5^3$ is False