Question

evaluate the expression.
\frac{4^{3}}{4^{5}}
the value of the expression is \square.

Explanation:

Step1: Recall exponent rule

For \( \frac{a^m}{a^n} \), use \( a^m\div a^n = a^{m - n} \). Here \( a = 4 \), \( m = 3 \), \( n = 5 \).

Step2: Apply the rule

\( \frac{4^3}{4^5}=4^{3 - 5}=4^{-2} \).

Step3: Simplify \( 4^{-2} \)

Using \( a^{-n}=\frac{1}{a^n} \), \( 4^{-2}=\frac{1}{4^2}=\frac{1}{16} \).

Answer:

\(\frac{1}{16}\)