The fundamental principles of algebra are not too difficult to learn. Adding and subtracting to solve for variables can even be fun. However, as the equations become longer and more complicated, they can begin to look increasingly confusing. Multiplication, fractions and exponents raise the difficulty level as each new concept is added. Fortunately, by following some basic rules and completing the steps in the right order you can easily solve the most complicated problems.
Multiply the exponents outside the parentheses by the exponents on each of the base numbers that make up the fraction. If there is no exponent shown then the exponent is 1. Here is an example of how to multiply fractions containing exponents:
(x^2/y)^3 * (x^3/z^2)^2 = a
(x^(23)/y^(13)) (x^(32)/z^(2*2)) = a
(x^6/y^3) * (x^6/z^4) = a
Combine like variables when possible. In this example, multiply the numerators together and the denominators together. The numerators are the numbers or variables on top of the fractions and the denominators are the ones on bottom.
(x^6 x^6) / (y^3 z^4) = a
Simplify the equation by multiplying like variables together. Combine the x variable by adding the exponents together.
(x^(6+6) / (y^3 * z^4) = a
x^12 / (y^3 * z^4) = a
Tips & Warnings
- Always simplify as much as possible.
- Solve for the variable if only one variable is used in the equation.
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