Answer:
[tex]-\frac{3\sqrt[3]{t} }{2}[/tex]
Step-by-step explanation:
1: Write g(t) as y, resulting in [tex]y=-\frac{8}{27}t^3[/tex]
2: Interchange the variables y and t, resulting in [tex]t=-\frac{8}{27}y^3[/tex]
3: Multiply both sides by 27, resulting in [tex]27t=-8y^3[/tex]
4: Divide both sides by -8, resulting in [tex]-\frac{27t}{8}=y^3[/tex]
5: Find the cube root of both sides, resulting in [tex]\sqrt[3]{-\frac{27t}{8} }=y[/tex]
6: Apply a radical rule, resulting in [tex]-\sqrt[3]{\frac{27t}{8} } =y[/tex]
7: Apply another radical rule, resulting in [tex]-\frac{\sqrt[3]{27t} }{\sqrt[3]{8} } =y[/tex]
8: Simplify the denominator, resulting in [tex]-\frac{\sqrt[3]{27t} }{2} =y[/tex]
9: Apply yet another radical rule, resulting in [tex]-\frac{\sqrt[3]{27}\sqrt[3]{t} }{2} =y[/tex]
10: Simplify [tex]\sqrt[3]{27}[/tex], resulting in [tex]-\frac{3\sqrt[3]{t} }{2} =y[/tex]
