Answer
$\dfrac{1}{\sqrt[4]{t^3}}$ or $\dfrac{1}{\left(\sqrt[4]{t}\right)^3}$
Work Step by Step
We are asked to rewrite the exponent into radical form:
$t^{-\frac{3}{4}}$
Recall the basic property of negative exponents (pg. 383):
$a^{-m}=\frac{1}{a^m}$
Applying this property, we get:
$t^{-\frac{3}{4}}=\dfrac{1}{t^{\frac{3}{4}}}$
Next, recall the rational exponent property (pg. 382):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$
Applying this property to our equation ($m=3$, $n=4$, $a=t$), we get:
$\dfrac{1}{t^{\frac{3}{4}}}=\dfrac{1}{\sqrt[4]{t^3}}$ or $\dfrac{1}{(\sqrt[4]{t})^3}$
