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