To simplify the expression
[tex]\[
\frac{4^9}{4^3}
\][/tex]
we can use the properties of exponents. When dividing powers with the same base, we subtract the exponents. Therefore:
[tex]\[
\frac{4^9}{4^3} = 4^{9-3} = 4^6
\][/tex]
Next, we need to calculate the value of [tex]\(4^6\)[/tex]. This means multiplying 4 by itself 5 more times:
[tex]\[
4^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4
\][/tex]
After performing this multiplication, we find that:
[tex]\[
4^6 = 4096
\][/tex]
So, the simplified value of the expression
[tex]\[
\frac{4^9}{4^3}
\][/tex]
is [tex]\(4096\)[/tex].
[tex]\[
\boxed{4096}
\][/tex]
