To evaluate the expression \( 1 + 5 \div 1^3 \), we follow the order of operations (PEMDAS/BODMAS):
- Parentheses/Brackets
- Exponents/Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Let's break down the expression step by step:
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Calculate the exponent: \[ 1^3 = 1 \]
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Now substitute back into the expression: \[ 1 + 5 \div 1 \]
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Perform the division: \[ 5 \div 1 = 5 \]
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Substitute back into the expression: \[ 1 + 5 \]
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Finally, perform the addition: \[ 1 + 5 = 6 \]
Thus, the value of the expression \( 1 + 5 \div 1^3 \) is \(\boxed{6}\).