Question

Tori examined the pattern of exponents in the table.

Powers of 6
Value
6 cubed
216
6 squared
36
6 Superscript 1
6
6 Superscript 0
1
6 Superscript negative 1
a
6 Superscript negative 2
b

Based on the pattern, which statements are true? Check all that apply.
The value of a is –6.
The value of b is StartFraction 1 Over 36 EndFraction.
As the exponents decrease, each previous value is divided by 6.
As the exponents increase, 6 is added to each previous value.
If the table was extended, the value of 6 Superscript negative 3 would be StartFraction 1 Over 216 EndFraction.

Answer 1

True statements:
- The value of b is 1/36. (6^-2 = 1/36.)
- As the exponents decrease, each previous value is divided by 6. (E.g. 216 → 36 → 6 → 1 → 1/6 → 1/36.)
- If extended, 6^-3 = 1/216. (Each step down divides by 6.)

False statements:
- a is not −6 (6^-1 = 1/6).
- Exponents increasing do not add 6; they multiply the previous value by 6.