Answer:
The value of b is [tex]\frac{1}{y^7}[/tex].
Step-by-step explanation:
Here the given expression is,
[tex](yb)^4=\frac{1}{y^{24}}[/tex]
[tex]y^4b^4=\frac{1}{y^{24}}[/tex] ( Using [tex](ab)^m=a^mb^m[/tex] on left side )
[tex]y^4b^4y^24 = 1[/tex] ( By cross multiplication )
[tex]y^{4+24}b^4=1[/tex] ( Using [tex]a^ma^n=a^{m+n}[/tex] on left side )
[tex]y^{28}b^4=1[/tex]
[tex]b^4=\frac{1}{y^{28}}[/tex]
[tex]b=(\frac{1}{y^{28}})^{\frac{1}{4}}[/tex] ( [tex]a^m=b^n\implies a=b^\frac{n}{m}[/tex] )
[tex]b=\frac{1^{\frac{1}{4}}}{(y^{28})^\frac{1}{4}}[/tex] ( [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex] )
[tex]b=\frac{1}{y^{28\times \frac{1}{4}}}[/tex] ( [tex](a^m)^n=a^{m\times n}[/tex] )
[tex]b=\frac{1}{y^7}[/tex]
