(5/13)11 × (5/13)19 ÷ (5/13)30 = ?

Concept

When powers of the SAME base are multiplied, their exponents are added; when divided, the exponent of the divisor is subtracted. That is, am × an ÷ ap = am + n − p. Any non-zero base raised to the power 0 equals 1: a0 = 1.

Application

1. All three factors share the same base 5/13, so combine the exponents: (5/13)11 × (5/13)19 ÷ (5/13)30.

2. Add the exponents of the multiplied factors: 11 + 19 = 30.

3. Subtract the exponent of the divisor: 30 − 30 = 0, giving (5/13)0.

4. Any non-zero quantity raised to the power 0 is 1, so (5/13)0 = 1.

Cross-check

Independently, (5/13)11 × (5/13)19 = (5/13)30, and dividing a quantity by itself gives 1 — confirming the result is exactly 1.