# Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises - Page 83: 47

$\color{blue}{-\dfrac{12}{5}}$

#### Work Step by Step

Simplify using the PEMDAS rule for order of operations. The PEMDAS rule summarizes the order of operations: First Priority; P - parentheses or grouping symbols Second Priority: E - exponents Third Priorirty: M/D - multiplication or division, whichever comes first from the left Fourth Priority: A/S - addition or subtraction, whichever comes first from the left Simplify within the parentheses/grouping symbols to obtain: $=\dfrac{6(-4)-3^2(-2)^3}{-5(-2+6)} \\\dfrac{6(-4)-3^2(-2)^3}{-5(4)}$ Apply the exponents: $=\dfrac{6(-4)-9(-8)}{-5(4)}$ Perform the multiplications: $=\dfrac{-24-(-72)}{-20}$ Perform the subtraction then simplify: $=\dfrac{-24+72}{-20} \\=\dfrac{48}{-20} \\=\color{blue}{-\dfrac{12}{5}}$

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