5^m×5^-2=5^3. Find the value of "m"
Posted by: Navjot s. on 06.02.2020
We hve to use law of exponents which states that a^m* a^n=a^(m+n)
So if we use this law then a=5 and n=-2 as bases are same so
we can write m-2=3
Please see the attachment below
Given, 5^m x 5^-2 = 5^3
thus, 5^m x 1/5^2 = 5^3
or, 5^m = 5^3 x 5^2
or, 5^m = 5^5
thus, m = 5
Ans. m = 5
Solution: 5^m*5^(-2) = 5^3
So, 5^m = 5^(3+2)
=> 5^m = 5^5 .
=> m = 5
asthe base is same ie 5 on LHS powers will get added
so we get
as base is common on LHS and RHS we can remove the base and equate the powers so we get
Ans: LHS= 5^m* 5^(-)2= 5^(m-2) (as per laws of indices)
RHS = 5^3
Therfore 5^(m-2)= 5^3
The two expressions are equal and their bases are also equal.Hence the indices must also be equal.
Hence m-2= 3 or m=5
Answer is m=5
question 5^m*5^-2=5^3 find value of m?
as we know that m^a*m^b=m^(a+b) formula
from herer m-2=3
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