To find the value of b needed for the expression to have a value of 81, we can substitute a = 4 and set the expression equal to 81:
12(4)^3b^7(4b)^-4 = 81
Since (4)^3 = 4^3 = 4*4*4 = 64, and (4b)^-4 = 1/(4b)^4 = 1/(4^4*b^4) = 1/(256b^4), we can rewrite the equation as:
12*64b^7/(256b^4) = 81
Simplifying the expression by canceling common factors and combining terms:
(12*64)/(256)b^(7-4) = 81
192/256 b^3 = 81
Dividing both sides of the equation by 192/256:
b^3 = 81 * 256 / 192
b^3 = 108
Therefore, the value of b needed for the expression to have a value of 81 when a = 4 is b = 108.
In the expression below if a = 4, what value of b is needed for the expression to have a value of 81?
12a^3b^7(ab)^-4
1 answer