12a^3b^7 * (ab)^-4 = 81

Answer 1

To solve this equation, let's simplify the left side of the equation first:

12a^3b^7 * (ab)^-4

Using the rule that (ab)^n = a^n * b^n, we can rewrite the expression as:

12a^3b^7 * a^-4 * b^-4

Now, we can combine like terms:

12a^(3+(-4)) * b^(7+(-4))

12a^(-1) * b^3

Next, we can rewrite the expression using the rule that a^-n = 1/a^n:

12 * 1/a * b^3

Simplifying further, we have:

12b^3/a

Now, we can set this expression equal to 81 and solve for a and b:

12b^3/a = 81

Multiplying both sides of the equation by a:

12b^3 = 81a

Dividing both sides of the equation by 12:

b^3 = (81a)/12

Simplifying the right side:

b^3 = 6.75a

Taking the cube root of both sides to solve for b:

b = (6.75a)^(1/3)

So, the value of b is given by (6.75a)^(1/3).