The value of [(10)150 ÷ (10)146] is:

Concept

For any nonzero base a, the quotient rule of exponents states that when dividing two powers with the same base, subtract the exponents: am ÷ an = a(m − n). This turns a division of large powers into a simple subtraction.

Application

1. Here the base is 10, with exponents 150 and 146.

2. Apply the quotient rule: (10)150 ÷ (10)146 = (10)(150 − 146) = (10)4.

3. Evaluate the power: (10)4 = 10 × 10 × 10 × 10 = 10000.

Cross-check

Multiply the result back by the smaller power: (10)4 × (10)146 = (10)150, which matches the original numerator — confirming the value is 10000.