Answer:
b = -6
Step-by-step explanation:
Apply the exponent rule that [tex]\frac{1}{x^{n}} = x^{-n}[/tex]
In this case, [tex]\frac{1}{y^{24}} = y^{-24}[/tex]
Set that equal to [tex](y^{b})^{4}[/tex]:
[tex](y^{b})^{4} = y^{-24}[/tex]
Apply the exponent rule that [tex](x^{m})^{n} = x^{mn}[/tex] so now you get:
[tex]y^{4b} = y^{-24}[/tex]
Since the base is y for both sides of the equation, just set the exponents equal to each other and solve for b.
4b = -24
divide each side by 4 to get:
b = -6
