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Exponent Laws

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 base x = the exponent. Other Properties of Exponents.

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Exponent Laws

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  1. Exponent Laws

  2. 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”. • bx • b = the base x = the exponent

  3. 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.

  4. Multiplying Powers with the SAME Base • Product of a Power • When you multiply a power with the same base, you add the exponents. • am x an = a m+n “a” is the base and “m” and “n” are the exponents. You need to show your work in the following format. • 23 x 24 = 2 (3+4) = 2 7

  5. Dividing Powers with the Same Base Quotient of Powers When you divide powers with the same base, you subtract the exponents. a4 ÷ a3 = a 4- 3 24 ÷ 23 = 2 (4- 3) = 21

  6. 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) • (23)4 = 2 (3x 4) = 212

  7. Power of a Product • When you are finding a power of a product , each number in the brackets is affected. • (ab)m = ambm • ( when there is no sign , remember that the operation is multiplication SO “ab” is “a” times “b”) • ( 3 x 6 )3 = 33 x 63 • 183 = 27 x 216 • 5832 = 5832

  8. Power of a Product cont’d • The opposite is also important. • If you have 45 x 65 , 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 245

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

  10. Combining Operations • If you have more than one operation to do , you will need to use your BEDMAS rules. • (45 64)5 (4  63)6 • (45)5 x (64)5  46 x (63)6 • = 4(25-6) X 6 (20 -18) • 4 19 x 62

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