Answer
$\frac{1}{t^{14}}$
Work Step by Step
We start with the given expression: $(t^2)^{-2}(t^2)^{-5}$
We simplify according to the order of operations:
First, we simplify powers: To raise a power to a power, we multiply the exponents: $t^{2\times-2}t^{2\times-5}=t^{-4}t^{-10}$
Next, we multiply. To multiply powers with the same base, we add the exponents. $t^{-14}$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression:
$\frac{1}{t^{14}}$
