The value of b is -6.
Explanation:
The expression is ![\left(y^{b}\right)^{4}=\frac{1}{y^{24}}](https://tex.z-dn.net/?f=%5Cleft%28y%5E%7Bb%7D%5Cright%29%5E%7B4%7D%3D%5Cfrac%7B1%7D%7By%5E%7B24%7D%7D)
To determine the value of b, we shall solve the expression.
Applying exponent rule,
, we get,
![y^{4b}=\frac{1}{y^{24}}](https://tex.z-dn.net/?f=y%5E%7B4b%7D%3D%5Cfrac%7B1%7D%7By%5E%7B24%7D%7D)
Applying exponent rule,
, we have,
![y^{4b}=y^{-24}](https://tex.z-dn.net/?f=y%5E%7B4b%7D%3Dy%5E%7B-24%7D)
The expression is of the form,
then ![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
Applying this rule, we get,
![4b=-24](https://tex.z-dn.net/?f=4b%3D-24)
Dividing both sides by 4, we have,
![b=-6](https://tex.z-dn.net/?f=b%3D-6)
Hence, the value of b is -6.