Question

What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24 Baseline EndFraction?

Answer 1

b

Step-by-step explanation:

did it on edge got it right

Answer 2

The value of b is -6.

Step-by-step explanation:

The expression is
`\left(y^(b)\right)^(4)=(1)/(y^(24))`

To determine the value of b, we shall solve the expression.

Applying exponent rule,
`\left(a^(b)\right)^(c)=a^(b c)`, we get,

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

Applying exponent rule,
`(1)/(a^(b))=a^(-b)`, we have,

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

The expression is of the form,
`a^(f(x))=a^(g(x))` then
`f(x)=g(x)`

Applying this rule, we get,

`4b=-24`

Dividing both sides by 4, we have,

`b=-6`

Hence, the value of b is -6.