Question

Which expression is equivalent to 1/49?

Answer 1

Expression is equivalent to 1/49

Option A

`\begin{gathered} 7^(-1)\text{ }*7^(-1)=7^(-1+(-1))\text{ (indices }*\text{ means +)} \\ 7^(-2)\text{ = }(1)/(7^2) \\ 7^(-1)\text{ }*7^(-1)=\text{ }(1)/(49) \\ \text{Option A is correct} \end{gathered}`

Option B

`\begin{gathered} 7^8\text{ }*7^(-6)=7^(8+(-6))\text{ (indices }*\text{ means +)} \\ 7^(8-6)=7^2\text{ = 49} \\ \text{ }7^8\text{ }*7^(-6)\text{ = 49} \\ \text{49 Option B is wrong} \end{gathered}`

Option C

`\begin{gathered} 7^(-5)\text{ }*7^3=7^(-5+3)\text{ (indices }*\text{ means +)} \\ 7^(-2)=\text{ }(1)/(7^2) \\ 7^(-5)\text{ }*7^3=\text{ }(1)/(49) \\ \text{Option C is correct} \end{gathered}`

Option D

`\begin{gathered} 7^7\text{ }*7^(-9)=7^(7+(-9))\text{ (indices }*\text{ means +)} \\ 7^(-2)=\text{ }(1)/(7^2) \\ 7^7\text{ }*7^(-9)=(1)/(49) \\ \text{Option D is correct} \end{gathered}`

Option E

`\begin{gathered} 7^(-2)\text{ }*7^4=7^(-2+4)\text{ (indices }*\text{ means +)} \\ 7^2\text{ = 49} \\ 7^(-2)\text{ }*7^4=\text{ 49} \\ \text{Option E is wrong} \end{gathered}`

Hence the expression equivalent to 1/49 are Option A,C & D