  Question:

5^m×5^-2=5^3. Find the value of "m"

Posted by: Navjot s. on 06.02.2020 Vinayak S. from Mumbai
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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

m=5 • Like L
Laxmi S. from Burdwan
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5^m-2=5^3 m=3+2=5 Aritra D. from Kolkata
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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

S
Sakshi from Gurgaon
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M= 5 S
Suma V. from Kochi
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From the law of exponents as the base is same powers are also same Ans. is 5 S.Chandra from Kolkata
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Ans. m = 5

Solution: 5^m*5^(-2) = 5^3

So, 5^m = 5^(3+2)

=> 5^m = 5^5 .

=> m = 5 • Like

5^m*5^-2=5^3

asthe base is same ie 5 on LHS powers will get added

so we get

5^(m-2)=5^3

as base is common on LHS and RHS we can remove the base and equate the powers so we get

m-2=3

m=3+2

m=5 • Like

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

N
• Like
5
S
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question 5^m*5^-2=5^3 find value of m?

as we know that m^a*m^b=m^(a+b) formula

similerly 5^m*5^-2=5^(m-2)

so 5^(m-2)=5^3

from herer m-2=3

so m=3+2;

S
Sandhya V. from Kochi
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5^m×5^-2=5^3where m value is 5
R
Rupali M. from Bangalore
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5^m*5^-2=5^3 5^m=5^3/5^-2 5^m=5^(3-(-2)) 5^m=5^5 m=5
D
Darshita T. from Surat
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According to exponential law of powers and indices, when base is the same and in multiplication, powers will be added. So, 5^m+(-2)=5^3 when base is the same powers can b compared. So, m+(-2)=3 m-2=3 m=3+2 m=5
M
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We know that a^m X a^n = a^m+n Here a= 5, n= -2 There fore m should be 5 to get 5^3 So the value of m is 5

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