Exponents represent shorthand notations of repeated multiplications, often written with the number or variable to be multiplied followed by a superscript value for the number of multiplications. The equation x times x times x times x can be rewritten as (xxxx) or x4 (note that the four is written as a superscript but may not be displayed). Exponents are read as the value to a given power, with the previous example read as “x to the fourth power”. Numbers or variables raised to the second power are simply called squared, and numbers raised to the third power are termed cubed. Multiplying and dividing exponents of similar variables or numbers only requires basic arithmetic skills of adding, subtracting and multiplying.
Multiply exponents by adding the exponents together. For example, x to the fifth power multiplied by x to the fourtth power equals x to the ninth power (x5 + x4 = x9), or (xxxxx)(xxxx) = (xxxxxxxxx).
Divide exponents by subtracting the exponents from each other. The equation x to the ninth power divided by x to the fifth power simplifies to x to the fourth power (x9 – x5 = x4), or (xxxxxxxxx)/(xxxxx) = (xxxx).
Simplify an exponent raised to another power by multiplying the exponents together. Simplifying x to the third power raised to the fourth power produces x to the 12th power [(x3)4 = x12], or (xxx)(xxx)(xxx)(xxx) = (xxxxxxxxxxxx).
Remember that any number to the 0th power equals one, meaning x to any power raised to the 0th power simplifies to one. Examples include x0 = 1, (x4)0 = 1, and (x5y3)0 = 1.
Note that equations with different variables such as x squared multiplied by y cubed (x2y3) cannot be combined to produce xy to the sixth power. This equation is already simplified. However, if the entire equation of x squared multiplied by y cubed is then squared, each of the variables is simplified separately, resulting in x to the fourth power multiplied by y to the sixth power (x2y3)2 = x4y6, or (xxxx)(yyyyyy).