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Answer:

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Apply the exponent rule that $\frac{1}{x^{n}} = x^{-n}$

In this case, $\frac{1}{y^{24}} = y^{-24}$

Set that equal to $(y^{b})^{4}$ :

$(y^{b})^{4} = y^{-24}$

Apply the exponent rule that $(x^{m})^{n} = x^{mn}$ so now you get:

$y^{4b} = y^{-24}$

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

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