Question

Solve the equation X to the power of m multiplied by x to the power 2 to the power of 3 multiplied by k to the power 3 to the power of 5 equals x to the power of 21 k to the power of 15.

Answer 1

To solve the exponential equation, we applied the rule of multiplying exponents and the property of adding exponents. The equation simplified to m + 8 = 21 for the variable x, leading us to conclude that m = 13.

Step-by-step explanation:

The equation that needs to be solved is expressed using exponents. We have an equation where x is raised to two different powers that are subsequently multiplied, and similarly, k is raised to two different powers that are multiplied.

Step-by-step, we need to simplify the equation by applying the exponent rules. The equation can be written as:

xm × x2^3 × k3^5 = x21 × k15

Using the rule of exponents (power of a power), we multiply the exponents for x and k. So, the equation simplifies further to:

xm × x8 × k15 = x21 × k15

Next, since the bases are the same, we add the exponents on the left side of the equation:

xm+8 × k15 = x21 × k15

We see that the exponents of k are already the same, so we focus on the exponents of x.

m + 8 = 21

Solving for m:

m = 21 - 8

m = 13

So, m is found to be 13.