What can we do if two different bases have the same exponents?

In multiplication and division, when the bases are the same and the exponents are different, the exponents can be added or subtracted, respectively. For example, X raised to the third power times X raised to the second power is the same as X raised to the fifth power. read more

In other words, when the bases are the same, you find the new power by just adding the exponents: Powers of Different Bases. Caution! The rule above works only when multiplying powers of the same base. read more

If the exponents are different though the bases are same, for example- x^2*x^3 , then they can by multiplied as x^ (2+3) = x^5. However this rule does not apply with addition or subtraction, all you can do with these operations is take out something common, for example- x^3 - x Here, x^3 - x = x( x^2–1) = x(x+1)(x-1). read more