Question

is the statement (10^5)(4^5) = 14^5 true?

Answer 1

Before we can prove/disprove it, we need to solve the equation.

So firstly, solve the exponents: (100000)(1024) _ 537824

Next, multiply everything on the left side, and your answer will be 102400000 ≠ 537824.

In short, that statement is false.

Answer 2

$10^5 \cdot 4^5=(10\cdot4)^5=40^5\\\\ 40^5\not= 14^5 \implies \text{false}$