Question

Which expressions are equivalent to StartFraction 1 Over 81 EndFraction? Check all that apply.

Answer 1

The options are

$(A)8^{-1} (B)9^{-2} (C)\dfrac{9^8}{9^4} (D)\frac{9^8}{9^{10}} (E)9^{-6}\cdot 9^3 (F)9^5 \cdot 9^{-7$

Answer:

$(B)9^{-2} \\ (D)\frac{9^8}{9^{10}} \\ (F)9^5 \cdot 9^{-7$

Step-by-step explanation:

Given the fraction $\dfrac{1}{81}$

$\dfrac{1}{81}=\dfrac{1}{9^2}=9^{-2$

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

Option B= $9^{-2}$ which is equivalent

In Option D: $\frac{9^8}{9^10}=9^{8-10}=9^{-2}$

In Option F: $9^5 \cdot 9^{-7}=9^{5-7}=9^{-2}$

Therefore, Options B, D and F are equivalent.