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

Question

asked Nov 8, 2021 79.3k views

2 Answers

Pushparaj · Answer 1 · 2021-11-15T11:06:35+0000

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.