Final answer:
To simplify (A²)³ × (a⁴)², raise each expression inside the parentheses to its respective power, resulting in A⁶ and a⁸, and then multiply the results by adding the exponents to get A¶⁴ as the simplified form.
Step-by-step explanation:
To simplify the expression (A²)³ × (a⁴)², we need to apply the rules of exponents. Specifically, when we raise a power to a power, we multiply the exponents. So, for (A²)³, we multiply the exponents 2 and 3 to get A⁶. Similarly, for (a⁴)², we multiply the exponents 4 and 2 to get a⁸.
Next, we multiply these two results together. Since the base 'a' is the same, we can simply add their exponents according to the property of exponents that states when multiplying like bases, the exponents should be added. So, A⁶ × a⁸ gives us A¶⁴. This is the simplified form of the original expression.