(1/5)^-m=125^3m
Hint: Raise both sides to a power.
hint 2: 125 = 5^3
Thanks, I understand the right side but I don't understand in the left side with (1/5)^-m. My teacher said the answer is m=0 but how?????
1/5 = 5^-1
(1/5)^-m = 5^(-1 * -m) = 5^m
So, now you have
5^m = 125^3m = 5^9m
m = 9m
m = 0
To solve the equation (1/5)^-m = 125^3m, we need to find the value of m that satisfies the equation.
First, let's simplify both sides of the equation separately:
On the left side:
(1/5)^-m can be rewritten using the reciprocal property of exponents as (5/1)^m. This gives us:
(5/1)^m = 125^3m
Now, let's rewrite 125^3m as (5^3)^3m using the property that a^mn = (a^m)^n. This gives us:
(5/1)^m = (5^3)^3m
Since the bases on both sides are the same, we can equate the exponents:
m = 3(3m)
Multiplying 3 by 3m gives us:
m = 9m
Next, we need to isolate the variable m. Subtracting 9m from both sides of the equation:
m - 9m = 0
-8m = 0
Dividing by -8 on both sides gives us:
m = 0
Therefore, the solution to the equation (1/5)^-m = 125^3m is m = 0.