Question

find the value of m for which 5^m/5^-3=125

Answer 1

5^m/5^-3=5^3
=)5^m*5^3=5^3
=)bases are same, so we equate power
=)m+3=3
=)m=3-3
=)m=0

Answer 2

Answer:

The value of m is 0 .

Step-by-step explanation:

As given the expression in the question be as follow .

$\frac{5^{m}}{5^{-3}} = 125$

As

125 = 5 ³

Put in the above expression

$\frac{5^{m}}{5^{-3}} = 5^{3}$

Now by using the exponent property

$\frac{x^{a}}{x^{b}} = x^{a-b}$

Thus

$5^{m-(-3)} = 5^{3}$

$5^{m+3} = 5^{3}$

Now compare power of the above expression

m + 3 = 3

m = 3 - 3

m = 0

Therefore the value of m is 0 .