Question

Simplify to a single power of 5:

(5^4)^3

Answer 1

5^12

Explanation:

This is called the "Power of Powers rule." When you are doing this rule, the inside exponent inside the parenthesis (the ^4 in this case) multiplies with the one outside the parenthesis, like this: 5^4*3 = 12.

However, if there is a base number next to the exponent outside the parenthesis that is a different number than the one inside the parenthesis, this method will not work. (Example: (5^4)5^3)

Important note: Anytime you are combining exponents through any rule, the base number must be the same to be able to combine.