Question

What is the value of b in the equation (yb) 4= 1/y24

Answer 1

Answer:

The value of b is $\frac{1}{y^7}$.

Step-by-step explanation:

Here the given expression is,

$(yb)^4=\frac{1}{y^{24}}$

$y^4b^4=\frac{1}{y^{24}}$  ( Using $(ab)^m=a^mb^m$ on left side )

$y^4b^4y^24 = 1$             ( By cross multiplication )

$y^{4+24}b^4=1$               ( Using $a^ma^n=a^{m+n}$ on left side )

$y^{28}b^4=1$

$b^4=\frac{1}{y^{28}}$

$b=(\frac{1}{y^{28}})^{\frac{1}{4}}$   ( $a^m=b^n\implies a=b^\frac{n}{m}$ )

$b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}$  ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$b=\frac{1}{y^{28\times \frac{1}{4}}}$   ( $(a^m)^n=a^{m\times n}$ )

$b=\frac{1}{y^7}$

Answer 2

B=6/y^2 hope this helps