(x^m x b^3)^2(k^5)^3 = x^18 k^15

what is the value of m

1 answer

In order to determine the value of m, we need to simplify the left side of the equation.

First, let's expand the expression (k^5)^3:
(k^5)^3 = k^(5*3) = k^15

Now, substituting this into the original expression:
(x^m x b^3)^2 * (k^5)^3 = x^18 k^15

We can simplify further by distributing the square:
(x^m)^2 * (b^3)^2 * (k^5)^3 = x^18 k^15

Taking into account the powers of the exponents:
x^(m*2) * b^(3*2) * k^(5*3) = x^18 k^15

Simplifying the powers of the exponents:
x^(2m) * b^6 * k^15 = x^18 k^15

Since the expression on the left side only has x and k terms, the powers of x and k on both sides must be equal. Therefore, we have the following equation:

2m = 18

Solving for m:
2m = 18
m = 18/2
m = 9

Therefore, the value of m is 9.