Questions: (0.5--0.1 ÷ 0.2)^3

Solution Steps

To solve the expression \((0.5 - -0.1 \div 0.2)^{3}\), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, resolve the division inside the parentheses, then perform the subtraction, and finally raise the result to the power of 3.

First, we calculate the division in the expression: \[ -0.1 \div 0.2 = -\frac{1}{2} = -0.5 \]

Next, we substitute the result of the division back into the expression and perform the subtraction: \[ 0.5 - (-0.5) = 0.5 + 0.5 = 1.0 \]

Finally, we raise the result to the power of 3: \[ (1.0)^{3} = 1.0 \]

Final Answer