What is the value of m for the equation below?

Question

(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

Answer 1

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.