(4 points)

Question

Powers of 3 Value
3^3 27
3^2 9
3^1 3
3^0 a
3^-1 b
3^-2 1/9
3^-3 c
What is the pattern as the exponents decrease?
_________________________
What is the value of each variable?

a=________


b=________


c=________

Answer 1

In the given table, we can see how the values of \(3^n\) change as the exponent \(n\) decreases. The pattern is that each time the exponent decreases by 1, the value is divided by 3:

• Starting from \(3^3\) (which equals 27) and moving down:
  • \(3^2 = 27 / 3 = 9\)
  • \(3^1 = 9 / 3 = 3\)
  • \(3^0 = 3 / 3 = 1\) (thus \(a = 1\))
  • \(3^{-1} = 1 / 3 = \frac{1}{3}\) (thus \(b = \frac{1}{3}\))
  • \(3^{-2} = 1/9\) (already provided)
  • \(3^{-3} = 1 / 27\) (thus \(c = \frac{1}{27}\))

From this, we find the values for the variables:

• \(a = 1\)
• \(b = \frac{1}{3}\)
• \(c = \frac{1}{27}\)

Here are the answers:

a = 1
b = \(\frac{1}{3}\)
c = \(\frac{1}{27}\)