Question

Evaluating a Solution to Determine the Expressions
Which expressions are equivalent to StartFraction 1 Over 81 EndFraction? Check all that apply.
8-1
9-2
StartFraction 9 Superscript 8 Over 9 Superscript 4 EndFraction
StartFraction 9 Superscript 8 Over 9 Superscript 10 EndFraction
9-6 · 93
95 · 9-7

Answer 1

Interpreting notation like 9-2 as 9^(-2), the expressions equivalent to 1/81 are:

- 9-2 = 9^(-2) = 1/9^2 = 1/81 ✓
- (9^8)/(9^10) = 9^(8-10) = 9^(-2) = 1/81 ✓
- 9^5 · 9-7 = 9^(5+(-7)) = 9^(-2) = 1/81 ✓

The others are not:
- 8-1 = 8^(-1) = 1/8
- (9^8)/(9^4) = 9^(8-4) = 9^4 = 6561
- 9-6 · 9^3 = 9^(-6+3) = 9^(-3) = 1/729