Laws of Exponents: A power raised to a power

Next on the list is the one that baffles most students when it’s extended to real problems, and I’ll show you why.

Rule #3- (a^x)^y = a^x*y

Practically: (x²)³ = (x * x) * (x * x) * (x * x) = x⁶

Put simply: (x²)³ = x^2*3 = x⁶

As with Rules 1 and 2, the bases must be the same.

Now, you’ll remember I said that this seemingly simple rule trips up people when faced with a harder problem.

Example: (4xy²)³ = 4³ * x^1*3 * y^2*3 = 64x³y⁶

Most people forget they have to apply the exponent to the coefficient as well as the exponents in the expression.