Questions: Simplificar. (w^7)^-4 Escribir la respuesta sin utilizar exponentes negativos.

Solution Steps

To simplify the expression \((w^{7})^{-4}\), we need to apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). This will give us \(w^{7 \cdot (-4)}\). Then, we simplify the expression by multiplying the exponents. Finally, we express the result without negative exponents by using the property \(a^{-n} = \frac{1}{a^n}\).

We start with the expression \((w^{7})^{-4}\). According to the power of a power property, we can rewrite this as: \[ (w^{7})^{-4} = w^{7 \cdot (-4)} = w^{-28} \]

To express the result without negative exponents, we use the property that \(a^{-n} = \frac{1}{a^n}\). Thus, we can rewrite \(w^{-28}\) as: \[ w^{-28} = \frac{1}{w^{28}} \]

Final Answer