Question

please answer the value of m $5^{m} / 5^{3} = 3125$

Answer 1

Answer:

given the expression in the question be as follow .

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

5

−3

5

m

=125

As

125 = 5 ³

Put in the above expression

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

5

−3

5

m

=5

3

Now by using the exponent property

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

x

b

x

a

=x

a−b

Thus

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

m−(−3)

=5

3

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