Answer:
10¹²
Step-by-step explanation:
[tex]f(t) = \left [t(t^{2})\right ]^{-2}\\[/tex]
Start with the inner parentheses and work out.
1. Apply the product rule.
[tex]\left [t(t^{2})\right ]^{-2} = \left [t^{3}\right ]^{-2}[/tex]
2 . Apply the power rule
[tex]f(t) = \left [t^{3}\right ]^{-2} = t^{-6}[/tex]
3. Substitute the value of t
[tex]f(10^{-2}) = (10^{-2})^{-6}[/tex]
4. Apply the power rule.
[tex]10^{-2 \times (-6)} = \mathbf{10^{12}}[/tex]
