What is the value of m for the equation below?
(x^m ⋅ x^3)^2 (k^5)^3 = x^18 k^15
Answer Choices:
M = 5
M = 7
M = 4
M = 6
To solve this problem, we can use the rules of exponents.
First, let's simplify the left side of the equation.
(x^m ⋅ x^3)^2 = x^(m*2) ⋅ x^(3*2) = x^(2m) ⋅ x^6
(k^5)^3 = k^(5*3) = k^15
Therefore, our equation becomes:
x^(2m) ⋅ x^6 ⋅ k^15 = x^18 ⋅ k^15
Using the rule of exponents for multiplication, we know that x^a ⋅ x^b = x^(a+b). Therefore, we can equate the exponents of x on both sides of the equation:
2m + 6 = 18
Now, let's solve this equation for m:
2m = 18 - 6
2m = 12
m = 12/2
m = 6
So, the value of m is M = 6.