Question

which expression is equivalent to 1/49?

Answer 1

Expression is equivalent to 1/49

Option A

$\begin{gathered} 7^{-1}\text{ }\times7^{-1}=7^{-1+(-1)}\text{ (indices }\times\text{ means +)} \\ 7^{-2}\text{ = }\frac{1}{7^2} \\ 7^{-1}\text{ }\times7^{-1}=\text{ }\frac{1}{49} \\ \text{Option A is correct} \end{gathered}$

Option B

$\begin{gathered} 7^8\text{ }\times7^{-6}=7^{8+(-6)}\text{ (indices }\times\text{ means +)} \\ 7^{8-6}=7^2\text{ = 49} \\ \text{ }7^8\text{ }\times7^{-6}\text{ = 49} \\ \text{49 Option B is wrong} \end{gathered}$

Option C

$\begin{gathered} 7^{-5}\text{ }\times7^3=7^{-5+3}\text{ (indices }\times\text{ means +)} \\ 7^{-2}=\text{ }\frac{1}{7^2} \\ 7^{-5}\text{ }\times7^3=\text{ }\frac{1}{49} \\ \text{Option C is correct} \end{gathered}$

Option D

$\begin{gathered} 7^7\text{ }\times7^{-9}=7^{7+(-9)}\text{ (indices }\times\text{ means +)} \\ 7^{-2}=\text{ }\frac{1}{7^2} \\ 7^7\text{ }\times7^{-9}=\frac{1}{49} \\ \text{Option D is correct} \end{gathered}$

Option E

$\begin{gathered} 7^{-2}\text{ }\times7^4=7^{-2+4}\text{ (indices }\times\text{ means +)} \\ 7^2\text{ = 49} \\ 7^{-2}\text{ }\times7^4=\text{ 49} \\ \text{Option E is wrong} \end{gathered}$

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