Exponent Laws

Laws of Exponents Whenever we have variables which contain exponents with the same bases, we can do mathematical operations with them. These are called the “ Exponents Laws”. b x b = the basex = the exponent

Other Properties of Exponents Any single number or variable is always to the power of one (1) If you have a negative exponent, you use the reciprocal of the base. Notice,your exponent will then be positive.

Multiplying Powers with the SAME Base Product of a Power When you multiply a power with the same base, you add the exponents. a m x a n = a m+n “a” is the base and “m” and “n” are the exponents. You need to show your work in the following format. 2 3 x 2 4 = 2 (3+4) = 2 7

Dividing Powers with the Same Base Quotient of Powers When you divide powers with the same base, you subtract the exponents. a 4 ÷ a 3 = a ÷ 2 3 = 2 (4- 3) = 2 1

Raising a Power Power of a Power When you are raising a power by an exponent, you must, multiply the exponents. (a m ) n = a (m x n) (2 3 ) 4 = 2 (3 x 4) = 2 12

Power of a Product When you are finding a power of a product, each number in the brackets is affected. (ab) m = a m b m ( when there is no sign, remember that the operation is multiplication SO “ab” is “a” times “b”) ( 3 x 6 ) 3 = 3 3 x = 27 x = 5832

Power of a Product cont’d The opposite is also important. If you have 4 5 x 6 5, notice that the exponents are the SAME. You can now do the opposite. For example, you can now take the exponent from the problem and multiply the bases. Then you can use your exponent. ( 4 x 6 ) 5 which is 24 5

Power of a Quotient When you have a fraction, the exponent affects both the numerator AND the denominator.

Combining Operations If you have more than one operation to do, you will need to use your BEDMAS rules. (4 5  6 4 ) 5  (4  6 3 ) 6 (4 5 ) 5 x (6 4 ) 5  4 6 x (6 3 ) 6 = 4 (25-6) X 6 (20 -18) 4 19 x 6 2