Final answer:
To solve for the variable 'a' in the equation 4^8 * 4^2 = 4^a using the properties of exponents, simplify the expression by adding the exponents when the bases are the same, and then solve for 'a' by equating the exponents.
Step-by-step explanation:
To solve for the variable in the equation 4^8 * 4^2 = 4^a using the properties of exponents, we need to use the rule that states when multiplying two exponential expressions with the same base, you add their exponents. In this case, 4^8 can be written as (4^2)^4, so the equation becomes (4^2)^4 * 4^2 = 4^a. Now, we can simplify further using the rule that states when raising an exponential expression to another exponent, we multiply the exponents. Therefore, we have 4^(2*4) * 4^2 = 4^a. Simplifying the exponents, we get 4^8 * 4^2 = 4^a. Since the bases are equal, the exponents must also be equal. Therefore, a = 8 + 2, which is equal to 10.