Question

find the value of m for which average power 5 raise to power M divide by 5 raise to power minus 3 equals to 5 raise to power minus 2​

Answer 1

5 raise to power m is equals to 5 raise to -2 multiply 5 raise to -3

5 raise to m equals to 5 raise to -3+(-5)=-5

therefore ,5 raise to m equal to 5 raise to -5.

5 and 5 both side cut

so m = -5 or 1/5

Answer 2

The value of m is -5.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{5^m}{5^{-3}} = 5^{-2}$

We have to find the value of m such that it satisfies the above relation.

Exponent properties:

$\dfrac{x^a}{x^b} = x^{a-b}\\\\x^a \times x^b = x^{a+b}$

Solving, we get,

$\dfrac{5^m}{5^{-3}} = 5^{-2}\\\\5^m = 5^{-2}\times 5^{-3}\\5^m = 5^{-2-3}\\5^m = 5^{-5}\\\Rightarrow m = -5$

The value of m is -5.

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