Final answer:
To order 16 1/2, (-3)⁰, and (1/27)⁻¹/³, we convert each to a familiar form: (-3)⁰ is 1, (1/27)⁻¹/³ is 1/3, and 16 1/2 is 16.5. Therefore, from smallest to largest, the order is (1/27)⁻¹/³, (-3)⁰, 16 1/2.
Step-by-step explanation:
The question asks to order the numbers 16 1/2, (-3)⁰, and (1/27)⁻¹/³. To compare these, we need to understand what each expression represents:
- 16 1/2 is a mixed number, representing sixteen and a half, or 16.5.
- (-3)⁰ is an application of the exponent zero rule, which states that any non-zero number to the power of zero is equal to 1. So (-3)⁰ equals 1.
- (1/27)⁻¹/³ is a negative fractional exponent, meaning the cube root of 27, which is 3, taken to the power of -1, which is the reciprocal. Hence, (1/27)⁻¹/³ equals 1/3.
Now we can order them from smallest to largest:
- (1/27)⁻¹/³ = 1/3 (since one-third is smaller than one)
- (-3)⁰ = 1 (because any number to the power of zero is 1)
- 16 1/2 = 16.5 (which is larger than 1)