Answer
$\dfrac{1}{128}$
Work Step by Step
With $3.5=\frac{7}{2}$, the given expression can be written as:
$=4^{-\frac{7}{2}}$
Recall the basic exponent property (pg. 360):
$(a^m)^n=a^{mn}$
Using this property, we get:
$4^{-\frac{7}{2}}=(4^{\frac{1}{2}})^{-7}$
Recall that $\sqrt[n]{x}=x^{\frac{1}{n}}$.
Thus, the expression above can be written as:
$=(\sqrt{4})^{-7}$
Since $2^2=4$, then the expression above simplifies to:
$=(2)^{-7}$
Recall the basic exponent property (pg. 383):
$a^{-m}=\frac{1}{a^m}$
Applying this, we get:
$(2)^{-7}=\dfrac{1}{(2)^{7}}=\dfrac{1}{128}$
