Question

What is the value of b in the equation (y^b)^4 = 1/y^24?

Answer 1

`\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`

solve for "b"

Answer 2

Explanation:

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

`(y^b)^4 = 1/y^(24) )`

it simplifies to

`y^(4b) = 1/y^(24)`

`y^(4b) = y^(-24)`

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

`4b=-24\\b=(-24)/(4) \\b=-6`