Question

now its time to practice on your own simplify fully. \\((t^{-6} \cdot t^2)^3\\) use positive exponents only. enter your answer in the box.

Explanation:

Step1: Add exponents inside parentheses

When multiplying like bases, add exponents: $t^{-6} \cdot t^{2} = t^{-6+2} = t^{-4}$

Step2: Apply power of a power rule

Multiply exponents when raising a power to a power: $(t^{-4})^3 = t^{-4 \times 3} = t^{-12}$

Step3: Convert to positive exponents

A negative exponent means reciprocal: $t^{-12} = \frac{1}{t^{12}}$

Answer:

$\frac{1}{t^{12}}$