Question

Which expressions are equivalent to 1 / 36? check all that apply

Answer 1

the answer to this question is option b,c and f or options 2, 3 and 6

i'll explain how to get this with a law of indices

`a^(-m)=(1)/(a^m)`

1.

`\begin{gathered} 3^(-6)=(1)/(3^6) \\ \text{this option is incorrect} \end{gathered}`

2.

`\begin{gathered} 6^(-2)=(1)/(6^2)=(1)/(36) \\ \text{this is correct since the square of 6 is equal 36} \end{gathered}`

3.

`(6^3)/(6^5)=6^(3-5)=6^(-2)=(1)/(6^2)=(1)/(36)`

4.

`\begin{gathered} (6^2)/(6^(-1))=6^(2-(-1))=6^(2+1)=6^3 \\ \text{this option is incorrect} \end{gathered}`

5.

`6\cdot6^(-2)=6^(1+(-2))=6^(-1)=(1)/(6)`

6.

`6^(-9)\cdot6^7=6^(-9+7)=6^(-2)=(1)/(6^2)=(1)/(36)`