Statement Simplify: [(14)3⋅(23)3]−1⋅(16)−4\left[\left(\frac{1}{4}\right)^3 \cdot \left(\frac{2}{3}\right)^3\right]^{-1} \cdot \left(\frac{1}{6}\right)^{-4}[(41)3⋅(32)3]−1⋅(61)−4 Solution One applies the properties of powers; the exponent −1-1−1 inverts the fraction, and (16)−4=64\left(\tfrac{1}{6}\right)^{-4}=6^4(61)−4=64: =[143⋅2333]−1⋅64=[864⋅27]−1⋅64=[1216]−1⋅64=216⋅64=63⋅64=67=279936\begin{aligned} &= \left[\frac{1}{4^3}\cdot\frac{2^3}{3^3}\right]^{-1} \cdot 6^4 = \left[\frac{8}{64\cdot 27}\right]^{-1}\cdot 6^4 = \left[\frac{1}{216}\right]^{-1}\cdot 6^4 \\ &= 216 \cdot 6^4 = 6^3\cdot 6^4 = \boxed{6^7 = 279936} \end{aligned}=[431⋅3323]−1⋅64=[64⋅278]−1⋅64=[2161]−1⋅64=216⋅64=63⋅64=67=279936 Links Topics: Numbers and operations Concepts: Power · Properties of powers Skills: Calculate · Simplify Exercise type: Evaluating expressions