B. Does a12 x a4 = a8 x a8 for all values of a? Explain.

We can use the Laws of Exponent to rewrite both sides of the equation:

Let a¹² x a⁴ = a⁸ x a⁸

⇒        a¹²⁺⁴ = a⁸⁺⁸

             a¹⁶ = a¹⁶  ✅

⇒  a¹² x a⁴ = a⁸ x a⁸ is true for all values of a.

Explanation:

The equation a¹² x a⁴ = a⁸ x a⁸ is true because, on both the RHS and LHS of the equation, both terms in 'a' have exponents that when added (Law of Multiplication of Exponents) are equal to each other, i.e. 12+4 = 8 + 8.