Answer
$2$
Work Step by Step
When a fraction is raised to a power, the exponent applies to both the numerator as well as the denominator. Let's rewrite the problem to reflect this:
$=\dfrac{1^{-1/6}}{64^{-1/6}}$
We can break down the number $64$ into a smaller base raised to a power.
The number $64$ breaks down to base $2$ raised to the $6th$ power:
$=\dfrac{1^{-1/6}}{(2^{6})^{-1/6}}$
Since $1$ raised to any power is equal to $1$, then the numerator simplifies tp $1$
$=\dfrac{1}{2^{(6)(-1/6)}}$
Let us multiply the fractional exponent:
$=\dfrac{1}{2^{-6/6}}$
$=\dfrac{1}{2^{-1}}$
Simplified expressions cannot have negative exponents.
Use the rule $a^{-m}=\frac{1}{a^m}$ to obtain:
$=\dfrac{1}{\frac{1}{2}}$
$=1 \cdot 2\\
=2$
