The problem asks us to evaluate the expression $((-4)^3 \div (-2)^5) \times (-3)$.

ArithmeticOrder of OperationsExponentsInteger Arithmetic
2025/5/4

1. Problem Description

The problem asks us to evaluate the expression ((4)3÷(2)5)×(3)((-4)^3 \div (-2)^5) \times (-3).

2. Solution Steps

First, we evaluate (4)3(-4)^3:
(4)3=(4)×(4)×(4)=16×(4)=64(-4)^3 = (-4) \times (-4) \times (-4) = 16 \times (-4) = -64
Next, we evaluate (2)5(-2)^5:
(2)5=(2)×(2)×(2)×(2)×(2)=4×4×(2)=16×(2)=32(-2)^5 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) = 4 \times 4 \times (-2) = 16 \times (-2) = -32
Now, we substitute these values into the expression:
((4)3÷(2)5)×(3)=(64÷32)×(3)((-4)^3 \div (-2)^5) \times (-3) = (-64 \div -32) \times (-3)
Then, we evaluate 64÷32-64 \div -32:
64÷32=6432=2-64 \div -32 = \frac{-64}{-32} = 2
Finally, we multiply by 3-3:
2×(3)=62 \times (-3) = -6

3. Final Answer

-6

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