Which definitions or properties would you use to simplify the expression ( {4}^(8) * {4}^( - 4) {)}^( - 2) explain

Question

Which definitions or properties would you use to simplify the expression


`( {4}^(8) * {4}^( - 4) {)}^( - 2)`
explain

Answer 1

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.