To find the value of b needed for the expression to have a value of 81 when a = 4, we substitute the values into the expression and solve for b.
12(4)^3 b^7∙(4b)^(-4) = 81
12(64) b^7∙(4b)^(-4) = 81
768 b^7∙(4b)^(-4) = 81
Since the bases are the same, we can combine the exponents:
768 b^7∙4^(-4)b^(-4) = 81
768 b^7∙(1/4)^4b^(-4) = 81
Simplifying further:
768 b^7∙(1/256)b^(-4) = 81
768 b^7 / 256 b^4 = 81
Simplifying the right side:
3 b^7 / b^4 = 81
Dividing the exponents:
3 b^(7-4) = 81
3 b^3 = 81
Dividing both sides by 3:
b^3 = 27
Taking the cube root of both sides:
b = 3
Therefore, if a = 4, then b = 3 is needed for the expression to have a value of 81.
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)
1 answer