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

The options are

`(A)8^(-1) (B)9^(-2) (C)(9^8)/(9^4) (D)(9^8)/(9^(10)) (E)9^(-6)\cdot 9^3 (F)9^5 \cdot 9^{-7`

Answer:

`(B)9^(-2) \\ (D)(9^8)/(9^(10)) \\ (F)9^5 \cdot 9^{-7`

Explanation:

Given the fraction
`(1)/(81)`

`(1)/(81)=(1)/(9^2)=9^{-2`

Any option that gives a form equivalent to any of the above is valid.

Option B=
`9^(-2)` which is equivalent

In Option D:
`(9^8)/(9^10)=9^(8-10)=9^(-2)`

In Option F:
`9^5 \cdot 9^(-7)=9^(5-7)=9^(-2)`

Therefore, Options B, D and F are equivalent.