Answer: b = 81
Step-by-step explanation:
We will solve for the unknown variable, b, in the given equation.
Given:
[tex]\displaystyle b^{-\dfrac{3}{4}}=\frac{1}{27}[/tex]
Rewrite negative three-fourths:
[tex]\displaystyle (b^{-\frac{1}{4}})^3=\frac{1}{27}[/tex]
Take the cube root of both sides of the equation:
[tex]\displaystyle b^{-\frac{1}{4}}=\frac{1}{3}[/tex]
Move b into the denominator and change the variable to a positive:
[tex]\displaystyle \frac{1}{b^{\frac{1}{4}}} =\frac{1}{3}[/tex]
Cross-multiply:
[tex]\displaystyle b^{\frac{1}{4}} *1 =3*1[/tex]
[tex]\displaystyle b^{\frac{1}{4}} =3[/tex]
Raise both sides of the equation to the power of four:
[tex]b=81[/tex]
This gives us our answer, the unknown is b = 81.