Question

simplify. express your answer using exponents.
$(w^{-1}x^{-5}y^{4})^{-5}$

Explanation:

Step1: Apply power of a product rule

For a product \((abc)^n = a^n b^n c^n\), so \((w^{-1}x^{-5}y^{4})^{-5}= (w^{-1})^{-5}(x^{-5})^{-5}(y^{4})^{-5}\)

Step2: Apply power of a power rule

The power of a power rule is \((a^m)^n=a^{m\times n}\).
For \((w^{-1})^{-5}\), \(m = - 1\), \(n=-5\), so \((w^{-1})^{-5}=w^{(-1)\times(-5)} = w^{5}\)
For \((x^{-5})^{-5}\), \(m=-5\), \(n = - 5\), so \((x^{-5})^{-5}=x^{(-5)\times(-5)}=x^{25}\)
For \((y^{4})^{-5}\), \(m = 4\), \(n=-5\), so \((y^{4})^{-5}=y^{4\times(-5)}=y^{-20}\)
Combining these results, we get \(w^{5}x^{25}y^{-20}\)

Answer:

\(w^{5}x^{25}y^{-20}\)