The evaluation of the expression -4*5+((-1)²-4³) is -83, following the order of operations rule (PEMDAS/BEDMAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
To evaluate the given expression, -4*5+((-1)²-4³), we first apply the order of operations rule, also known as BEDMAS or PEMDAS: Brackets/parentheses, Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Following this order, we first attend to the Brackets: (-1)² is 1 and 4³ is 64. The expression now reads -4*5+(1 - 64).
Next, we do the subtraction within the parentheses, which is 1 - 64, yielding -63. Our expression now reads -4*5 + -63.
Now, let's multiply -4*5 which is -20. This makes our expression become -20 + -63.
Finally, we do the addition (keeping track of the negatives), which gives -20 + -63 = -83.
Therefore, -4*5+((-1)²-4³) equals -83.
Learn more about Order of Operations