In the expression 12a^3b^7•(ab)^-4 what value of b is needed for the expression to have a value of 81
To find the value of b, we need to set the expression equal to 81 and solve for b.
12a^3b^7•(ab)^-4 = 81
Since (ab)^-4 is equivalent to 1/(ab)^4, we can rewrite the expression as:
12a^3b^7 • 1/(ab)^4 = 81
Multiplying both sides of the equation by (ab)^4, we get:
12a^3b^7 = 81(ab)^4
Expanding (ab)^4 on the right side, we have:
12a^3b^7 = 81a^4b^4
Dividing both sides of the equation by a^3, we get:
12b^7 = 81a^4b^4/a^3
Simplifying the right side, we have:
12b^7 = 81ab
Dividing both sides of the equation by b, we get:
12b^6 = 81a
Dividing both sides of the equation by 12, we get:
b^6 = (81a)/12
Simplifying the right side, we have:
b^6 = 27/4a
Taking the sixth root of both sides, we get:
b = (27/4a)^(1/6)
Thus, the value of b needed for the expression to have a value of 81 is b = (27/4a)^(1/6).