To simplify the expression [tex]\(\left(3 w^5 x^{-4}\right)^{-3}\)[/tex] and write the answer using only positive exponents, follow these steps:
1. Apply the exponent to each factor inside the parentheses:
[tex]\[
(3 w^5 x^{-4})^{-3} = 3^{-3} \cdot (w^5)^{-3} \cdot (x^{-4})^{-3}
\][/tex]
2. Simplify each term individually:
- For [tex]\(3^{-3}\)[/tex]:
[tex]\[
3^{-3} = \frac{1}{3^3} = \frac{1}{27}
\][/tex]
- For [tex]\((w^5)^{-3}\)[/tex]:
[tex]\[
(w^5)^{-3} = w^{5 \cdot (-3)} = w^{-15}
\][/tex]
- For [tex]\((x^{-4})^{-3}\)[/tex]:
[tex]\[
(x^{-4})^{-3} = x^{-4 \cdot (-3)} = x^{12}
\][/tex]
3. Combine all the simplified terms:
[tex]\[
3^{-3} \cdot w^{-15} \cdot x^{12} = \frac{1}{27} \cdot w^{-15} \cdot x^{12}
\][/tex]
4. Write the final answer, ensuring all exponents are positive:
[tex]\[
\frac{1}{27} w^{-15} x^{12} = \frac{x^{12}}{27 w^{15}}
\][/tex]
Thus, the simplified expression is:
[tex]\[
\frac{x^{12}}{27 w^{15}}
\][/tex]
