The problem is to evaluate the expression $(-3)^8 \div (-3)^5$.

AlgebraExponentsAlgebraic simplification
2025/5/4

1. Problem Description

The problem is to evaluate the expression (3)8÷(3)5(-3)^8 \div (-3)^5.

2. Solution Steps

To solve the problem, we use the rule for dividing exponents with the same base:
am÷an=amna^m \div a^n = a^{m-n}
In this case, a=3a = -3, m=8m = 8, and n=5n = 5. Therefore, we have:
(3)8÷(3)5=(3)85=(3)3(-3)^8 \div (-3)^5 = (-3)^{8-5} = (-3)^3
Now, we evaluate (3)3(-3)^3:
(3)3=(3)×(3)×(3)=9×(3)=27(-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27

3. Final Answer

The final answer is -27.

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