Answer :

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.