Final answer:
To simplify (t⁶ x t⁶)³, you first add the exponents to get t¹², then cube the result to get t³⁶, which is the fully simplified expression.
Step-by-step explanation:
To simplify the expression (t⁶ x t⁶)³, one must understand the rules of exponents. When multiplying two exponential terms with the same base, you simply add the exponents. Since t⁶ and t⁶ have the same base of t, you add their exponents to get t¹² (which is t to the power of 12). Now, we have (t¹²)³, which means we need to cube the entire expression. When cubing an exponential term, one must multiply the exponent by 3. Therefore, (t¹²)³ = t¹²*3 = t³⁶. Thus, the fully simplified expression is t³⁶.