Respuesta :

[tex]\bf a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}}\\\\ -----------------------------\\\\ (y^b)^4=\cfrac{1}{y^{24}}\iff y^{b\cdot 4}=y^{-24}\implies y^{4b}=y^{-24} \\\\\\ \textit{bases are the same, exponents must be the same} \\\\\\ 4b=-24[/tex]

solve for "b"

Answer:

Step-by-step explanation:

Since we are solving an exponential equation so we first need to think about making the base of both sides of equation same .

[tex](y^b)^4 = 1/y^{24} )[/tex]

it simplifies to

[tex]y^{4b} = 1/y^{24}[/tex]

[tex]y^{4b} = y^{-24}[/tex]

Now base is same on both sides so we can equate the exponent

[tex]4b=-24\\b=\frac{-24}{4} \\b=-6[/tex]

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