1. We are asked to calculate the values of $x$, $z$, and $t$ given the equations $x^5 = -10.4858$, $z^4 = 1.749$, and $t^6 = -2.31306$. 2. To find $x$ in $x^5 = -10.4858$, take the fifth root: $$x = \sqrt[5]{-10.4858} = -\sqrt[5]{10.4858}$$ Calculate the fifth root of 10.4858: $$\sqrt[5]{10.4858} \approx 1.63$$ Since the base is negative and the exponent is odd, the result is negative: $$x \approx -1.63$$ 3. To find $z$ in $z^4 = 1.749$, take the fourth root: $$z = \sqrt[4]{1.749}$$ Calculate the fourth root: $$\sqrt[4]{1.749} \approx 1.15$$ Because the power is even, $z$ can be both positive or negative. We give the principal (positive) root: $$z \approx 1.15$$ 4. To find $t$ in $t^6 = -2.31306$, note that even powers cannot produce negative results over real numbers, so there is no real solution. However, if we consider complex numbers, the sixth root of a negative number has complex solutions. For simplicity, assuming real solutions only: No real solution for $t$ as $t^6$ cannot be negative. Final answers rounded to two decimal places: $$x \approx -1.63$$ $$z \approx 1.15$$ No real solution for $t$$