To find the value of b that would result in the expression having a value of 81 when a = 4, we can substitute the given values into the expression and solve for b.
Substituting a = 4 into the expression, we have:
12(4)^3 b^7(4b)^-4
Simplifying the expression:
12(64) b^7(4b)^-4
12 * 64 * b^7 * (4b)^-4
768b^7 * (4b)^-4
Since (4b)^-4 is the same as 1/(4b)^4, we can rewrite the expression as:
768b^7 / (4b)^4
To simplify this expression further, we can rewrite (4b)^4 as (4^4)b^4:
768b^7 / (4^4)b^4
768b^7 / 256b^4
Now, to find the value of b that would make this expression equal to 81, we can set up the equation:
768b^7 / 256b^4 = 81
Multiplying both sides of the equation by 256b^4, we have:
768b^7 = 81 * 256b^4
Dividing both sides of the equation by 768, we get:
b^7 = 81 * 256b^4 / 768
Simplifying:
b^7 = 81 * 256b^4 / 768
b^7 = 81 * b^4 / 3
Now, taking the seventh root of both sides of the equation to isolate b, we have:
b = (81 * b^4 / 3)^(1/7)
Using a calculator to evaluate this expression, we find that b ≈ 1.793.
Therefore, the value of b that is needed for the expression to have a value of 81 when a = 4 is approximately 1.793.
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
1 answer