What is the value of m for the equation below?
(x^m⋅x^3)^2(k^5)^3=x^18k^15
(1 point)
Responses
m=7
m is equal to 7
m=6
m is equal to 6
m=5
m is equal to 5
m=4
m is equal to 4
To find the value of m, we need to simplify the equation and compare the exponents.
Starting with the left side of the equation:
(x^m⋅x^3)^2(k^5)^3
Using the power rule for exponents, we multiply the exponents when raising a power to a power:
(x^(m*2)⋅x^(3*2))(k^(5*3))
Simplifying further:
(x^(2m)⋅x^6)(k^15)
Now, we can compare the exponents of x on both sides of the equation:
2m + 6 = 18
Solving for m, we subtract 6 from both sides of the equation:
2m = 18 - 6
2m = 12
Finally, we divide both sides of the equation by 2 to solve for m:
m = 12/2
m = 6
Therefore, the value of m is 6.