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

$a^{-m}=\frac{1}{a^m}$

1.

$\begin{gathered} 3^{-6}=\frac{1}{3^6} \\ \text{this option is incorrect} \end{gathered}$

2.

$\begin{gathered} 6^{-2}=\frac{1}{6^2}=\frac{1}{36} \\ \text{this is correct since the square of 6 is equal 36} \end{gathered}$

3.

$\frac{6^3}{6^5}=6^{3-5}=6^{-2}=\frac{1}{6^2}=\frac{1}{36}$

4.

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

5.

$6\cdot6^{-2}=6^{1+(-2)}=6^{-1}=\frac{1}{6}$

6.

$6^{-9}\cdot6^7=6^{-9+7}=6^{-2}=\frac{1}{6^2}=\frac{1}{36}$