Question

Solve $49\times {{\left( -7 \right)}^{m}}=-343$.

Answer 1

Hint: We can solve this problem in an easy way with the cube root of both sides. We will find the value of $m$ in this and this can be found if we solve both sides of the equation and then take cube root and then compare the powers of both or without taking cube root by comparing the powers directly and solve them. It will make this question easy and solvable.

Complete step by step answer:
According to our question it is asked to us to solve $49\times {{\left( -7 \right)}^{m}}=-343$. We will solve these problems very easily. As we know that if any term is given in multiplication form, then we always solve that as much as possible to find the values of the desired variable and for this question we will find $m$ in this and this can be found if we solve both the sides of the equation and then take cube root and then compare the powers of both or without taking cube root by comparing the powers directly and solve them. It will make this question easy and solvable. So, if we see our question, then:
$49\times {{\left( -7 \right)}^{m}}=-343$
We can also write this as:
$\begin{align}
  & {{7}^{2}}\times {{\left( -7 \right)}^{m}}={{\left( -7 \right)}^{3}} \\
 & \Rightarrow{{\left( -7 \right)}^{2+m}}={{\left( -7 \right)}^{3}} \\
\end{align}$
By comparing the powers of this, we get,
$\begin{align}
  & 2+m=3 \\
 & \Rightarrow m=3-2=1 \\
\end{align}$
So the value of $m$ is 1.

Note: While solving this type of question we have to be careful about the power when we convert them as a square form or as a cube form. For both terms, different - different powers are used. And then compare them with suitable methods for solving them.