49 ×(-7)^m = -343 find the value of m
Answers
Concept
If two numbers are equal and their base is also equal then their powers also must be equal. For example- if (a)^b = (a)^c, then b and c must be equal.
Given
49 ×(-7)^m = -343
Find
we need to find the value of m
Solution
We have
49 ×(-7)^m = -343
⇒ (-7)^m = -343/ 49
⇒ (-7)^m = -7
⇒ (-7)^m = (-7)^1
As we can see the bases on the left hand side and right hand side are same. Thus, we can equate their powers as they will also be same.
⇒ m = 1
Hence, the value of m is 1
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Answer:
1
Step-by-step explanation:
Concept= Indices
Given= The equation
To find= The value of unknown variable
Explanation=
We have been asked the question as 49 ×(-7)^m = -343 find the value of m.
Therefore we know that when we will equate the variable it will give a whole number.
Proceeding further we have,
49 ×(-7)^m = -343
we will first divide the equation by 49,
=> (-7)^m = -343/49
=> (-7)^m = -7
Now we see that there is nothing but only -7 as the value which will only come when the power of -7 is 1. So,
=> (-7)^m = -7^1
On comparing we get that m=1.
Hence the value of m is 1.
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