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One of the trickiest concepts in algebra involves the manipulation of exponents, or powers. Many times, problems will require you to simplify variables with exponents, or you will have to simplify an equation with exponents to solve it. To work with exponents, you need to know the basic exponent laws.

When a problem gives you two terms, or chunks, that do not have the exact same variables, or letters, raised to the exact same exponents, you cannot combine them. For instance, (4x^2)(y^3) + (6x^4)(y^2) could not be simplified (combined) further because the Xs and the Ys have different powers in each term.

If two terms have the same variables raised to the exact same exponents, subtract the second coefficient from the first and use the answer as the new coefficient for the combined term. The powers themselves do not change. For example, 5y^3 - 7y^3 would simplify to -2y^3.

When multiplying two terms (it does not matter if they are like terms), multiply the coefficients together to get the new coefficient. Then, one at a time, add the powers of each variable to make the new powers. If you multiplied (6x^3z^2)(2xz^4), you would end up with 12x^4z^6.

When a term that includes variables with exponents is raised to another power, raise the coefficient to that power and multiply each existing power with the second one to get the new one. For instance, (5x^6y^2)^2 would simplify to 25x^12y^4.

Anything raised to the power of 0 becomes the number 1. It does matter how complicated or big the term is. For instance, (5x^6y^2z^3)^0 would simplify to 1.

To divide when you have the same variable in the numerator and denominator, and the larger exponent is on top, subtract the bottom exponent from the top one and make the answer the new exponent of the variable on top. Then, eliminate the bottom variable. Reduce any coefficients like a fraction. If you were to do (3x^6)/(6x^2), you would end up with (x^4)/2.