If 10^m = 2 and 10^n = 3. Find the value of 10^(3m - n)
To solve this, let's first rewrite 10^(3m - n) using the given information:
10^(3m - n) = (10^m)^3 / 10^n
Since 10^m = 2 and 10^n = 3, we substitute these values into the expression:
(10^m)^3 / 10^n = 2^3 / 3 = 8 / 3
Therefore, the value of 10^(3m - n) is 8/3.
To find the value of 10^(3m - n) given that 10^m = 2 and 10^n = 3, we can substitute the given values into the equation.
First, let's substitute the value of 10^m = 2 into the expression 10^(3m - n):
10^(3m - n) = 10^(3m) / 10^n
Since 10^m equals 2, we can substitute it into the equation:
10^(3m) = (10^m)^3 = 2^3 = 8
Now, let's substitute the value of 10^n = 3 into the expression:
10^(3m - n) = 8 / 10^n = 8 / 3
Therefore, the value of 10^(3m - n) is 8/3.
To find the value of 10^(3m - n), we first need to express it in terms of the given information.
We know that 10^m = 2 and 10^n = 3. Let's use these equations to find the value of 10^(3m - n).
1. Begin by raising both sides of the equation 10^m = 2 to the power of 3:
(10^m)^3 = 2^3
Simplifying, we get:
10^(3m) = 8
2. We can rewrite 8 as 2^3, so we have:
10^(3m) = 2^3
3. Now, we can substitute the value of 10^(3m) into 10^(3m - n):
10^(3m - n) = (10^(3m))/(10^n)
Plugging in the known values, we get:
10^(3m - n) = (8)/(3)
Therefore, the value of 10^(3m - n) is 8/3.