How can we simplify various expressions using exponents?

The following are ways to solve simple mathematical expressions with the same base:

To multiply two numbers with different exponents, add the exponents:
(x²)(x⁴) = (xx)(xxxx) = xxxxxx = x²⁺⁴ = x⁶

To raise a number with a power, multiply the exponents:
(x³)³ = (x³)(x³)(x³) = (xxx)(xxx)(xxx) = xxxxxxxxx = x^(3x3) = x⁹

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