How to Use Properties of Exponents in Algebra 2
- 1). Figure out what the operation is that is taking place between the variables (letters). It may seem like common sense to look at the exponents first, but it is actually the operation between the variables themselves that determines what you should do. For instance, if you see X^3 + X^4, it is the "+" between the X's that you must focus on.
- 2). If the operation sign between the variables is a plus or a minus, then you must next check whether or not the exponents for each variable are the same. If they are the same, combine the different terms by adding or subtracting the coefficients (numbers in front) of each together. This is called "combining like terms." The terms are "alike" because they all have the same power. The power itself does not change; only the coefficient does. For example, 4X^3 + 5X^3 becomes 9X^3 and 8X^5 - 2X^5 turns into 6X^5.
- 3). If the operation between the variables is addition or subtraction but the exponents do not match, do nothing. These terms are not alike and cannot be simplified.
- 4). If the operation between the variables is multiplication, then multiply the coefficients and add the two exponents together to make the new exponent. If you have 4X^3 x 2X^2, you would end up with 8X^5.
- 5). If you see that the operation between the variables is division, subtract the second exponent from the first to make the new exponent. Divide the first coefficient by the second coefficient to get the new one. For instance, 10X^8/5X^2 becomes 2X^6.
- 6). If the variable and its exponent are being raised to another power, as with (3X^4)^3, then multiply the two exponents together to make the new exponent. To find the new coefficient, raise the old coefficient to the outside power. In this case, you would have 27X^12.