Question

In the expression below if a = 4, what value of b is needed for the expression to have a value of 81?

12a^3 b^7∙(ab)^(-4)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Given that a = 4, we can substitute a = 4 into the expression to simplify it:

12(4)^3 * b^7 * (4b)^(-4)
= 12(64) * b^7 * (4b)^(-4)
= 768b^7 * (4^-4)(b^-4)
= 768b^7 * 256b^-4
= 196,608b^(7-4)
= 196,608b^3

To find the value of b that will make the expression equal to 81, we set the expression equal to 81:

196,608b^3 = 81

Now, we solve for b:

b^3 = 81 / 196,608
b^3 = 1 / 2,432
b = (1 / 2,432)^(1/3)
b = 0.1

Therefore, the value of b needed for the expression to have a value of 81 when a = 4 is b = 0.1.