Reduce the Expression: 4³ × 4⁻⁵ Using Laws of Exponents

To solve the expression $4^3 \times 4^{-5}$, we need to apply the multiplication of powers rule. This rule states that when you multiply two powers with the same base, you can add their exponents. Mathematically, this is expressed as:

• $a^m \times a^n = a^{m+n}$

In our case, the base $a$ is 4, and the exponents $m$ and $n$ are 3 and -5, respectively.

Applying the rule:

$4^3 \times 4^{-5} = 4^{3 + (-5)}$

Simplifying the exponent:

$3 + (-5) = -2$

So, the expression simplifies to:

$4^{-2}$

This is the reduced form of the given equation.