Evaluate 1002.

Concept

Squaring a number means multiplying that number by itself: n2 = n × n. When the base is itself a power of 10 (100 = 102), the power rule (am)n = am×n gives a fast shortcut: the exponents multiply.

Application

1. Write the expression as repeated multiplication: 1002 = 100 × 100.

2. Multiply the leading digits: 1 × 1 = 1, then append the total count of zeros from both factors (2 + 2 = 4 zeros): 100 × 100 = 10,000.

3. Cross-check with the power rule: since 100 = 102, the exponents multiply (2 × 2 = 4), so 1002 = 104 = 10,000.

Cross-check

Reverse the operation: dividing 10,000 by 100 gives 100, confirming 100 × 100 = 10,000. The result also matches the pattern that 10n always renders as a 1 followed by n zeros — here 104 is 1 followed by four zeros.

Result

1002 = 10,000.