Question

Why$-4^3={\left(-4\right)}^3$?

Short answer

The multiply of negative numbers in odd power is negative.

Step-by-step solution

Step 1. Given Information.

Consider the right side.

${\left(-4\right)}^3$

Step 2. Explanation.

Rewrite the given expression ${\left(-4\right)}^3$.

$\begin{array}{rcl}{\left(-4\right)}^3& =& {\left(4·\left(-1\right)\right)}^3\\ & =& 4^3·{\left(-1\right)}^3\left[{\left(-1\right)}^3=1\right]\\ & =& 4^3\left(-1\right)\\ & =& -4^3\end{array}$

Thus, the given equation is true.