Question

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 the dashes as negative exponents (e.g. 9-2 = 9^-2):

1/81 = 9^-2. The expressions equivalent to 1/81 are:
- 9-2 because 9^-2 = 1/81.
- StartFraction 9^8 Over 9^10 EndFraction because 9^(8-10) = 9^-2.
- 9^5 · 9-7 because 9^(5-7) = 9^-2.

Not equivalent:
- 8-1 = 8^-1 = 1/8.
- StartFraction 9^8 Over 9^4 EndFraction = 9^(8-4) = 9^4.
- 9-6 · 9^3 = 9^(-6+3) = 9^-3 = 1/729.