If m^9/m^6 = 8, what is the value of m^5/m^2?
A:3
B:7
C:8
D:14
the same. You have just divided by m^4/m^4 = 1
The answer is 8
To solve this problem, we can simplify the left-hand side of the equation first:
m^9 / m^6 = m^(9-6) = m^3
Now we can substitute this value back into the equation:
m^3 = 8
To find m, we need to isolate it on one side of the equation. Taking the cube root of both sides gives us:
cube root of m^3 = cube root of 8
m = 2
Finally, let's substitute the value of m back into the equation we want to solve:
m^5 / m^2 = 2^5 / 2^2 = 32 / 4 = 8
Therefore, the value of m^5 / m^2 is 8.
The correct answer is C) 8.
To solve this problem, we need to simplify the expression m^9/m^6 = 8 and find the value of m^5/m^2.
Let's break it down step by step:
1. Divide the exponents: m^9/m^6
When dividing with the same base, subtract the exponents.
Therefore, m^9/m^6 = m^(9-6) = m^3.
2. Simplify the equation: m^3 = 8
Here, m^3 is equal to 8.
3. Find the value of m:
To isolate m, we need to take the cube root of both sides of the equation.
So, m = ∛8.
4. Simplify ∛8:
∛8 = 2, since 2 x 2 x 2 = 8.
5. Substitute the value of m in m^5/m^2:
Now, we need to find the value of m^5/m^2 using the calculated value of m.
m^5/m^2 = 2^5/2^2 = 32/4 = 8.
Therefore, the value of m^5/m^2 is 8.
So, the correct answer is C: 8.