Which definitions or properties would you use to simplify the expression

explain

Exponent multiplication and addition will simplify this expression.

Exponent Addition: a^b * a^c = a^ (b + c)

Exponent Multiplication: (a^ d) ^ e = a ^ (d * e)

Multiplication of 4^8 * 4^ (-4) is the same as adding exponents together:

4^ (8 - 4)

Which makes the expression simplify to (4^4). This expression is now to another exponent which is equivalent to multiplying exponents together:

(4^4) ^-2 = 4^ (4 * - 2) = 4 ^ - 8

The expression has been reduced to its simplest form.