The problem asks us to determine whether each of the given equations is true or false. The equations are $3^5 = 3 \times 5$, $3^5 = 5^3$, and $1^3 = 5^3$.

1. Problem Description

The problem asks us to determine whether each of the given equations is true or false. The equations are $3^5 = 3 \times 5$, $3^5 = 5^3$, and $1^3 = 5^3$.

2. Solution Steps

First equation: $3^5 = 3 \times 5$.

$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$.

$3 \times 5 = 15$.

Since $243 \ne 15$, the first equation is false.

Second equation: $3^5 = 5^3$.

$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$.

$5^3 = 5 \times 5 \times 5 = 125$.

Since $243 \ne 125$, the second equation is false.

Third equation: $1^3 = 5^3$.

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

$5^3 = 5 \times 5 \times 5 = 125$.

Since $1 \ne 125$, the third equation is false.

3. Final Answer

False

False

False