Question

Practice simplifying and evaluating powers with zero and negative exponents.
A 2-column table with 7 rows. Column 1 is labeled Power of 3 with entries 3 cubed, 3 squared, 3 Superscript 1, 3 Superscript 0, 3 Superscript negative 1, 3 Superscript negative 2, 3 Superscript negative 3. Column 2 is labeled Value with entries 27, 9, 3, a, b, StartFraction 1 Over 9 EndFraction, c.

Answer these questions about the powers of 3.

What is the pattern as the exponents decrease?

What is the value of each variable?
a =
b =
c =

Answer 1

Pattern: each time the exponent decreases by 1, the value is divided by 3 (equivalently, multiply by 1/3).

So the full sequence is 27, 9, 3, 1, 1/3, 1/9, 1/27.

Therefore:
a = 1
b = 1/3
c = 1/27