Answer :

Sure, let's simplify the given expression step-by-step.

The expression to simplify is:

[tex]\[ \frac{w^4\left(w^3\right)^5}{\left(w^5\right)^2} \][/tex]

1. Simplify the exponentiation inside the parentheses:
- [tex]\((w^3)^5\)[/tex] can be simplified using the power rule [tex]\((a^m)^n = a^{mn}\)[/tex].
[tex]\[ (w^3)^5 = w^{3 \cdot 5} = w^{15} \][/tex]

- [tex]\((w^5)^2\)[/tex] can also be simplified similarly.
[tex]\[ (w^5)^2 = w^{5 \cdot 2} = w^{10} \][/tex]

2. Substitute these simplified forms back into the original expression:
[tex]\[ \frac{w^4 \cdot w^{15}}{w^{10}} \][/tex]

3. Combine the exponents in the numerator using the product rule [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:
[tex]\[ w^4 \cdot w^{15} = w^{4+15} = w^{19} \][/tex]

So the expression now looks like:
[tex]\[ \frac{w^{19}}{w^{10}} \][/tex]

4. Simplify the fraction using the quotient rule [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[ \frac{w^{19}}{w^{10}} = w^{19-10} = w^9 \][/tex]

Thus, the simplified form of the given expression is:

[tex]\[ \boxed{w^9} \][/tex]