Properties of Exponents – Part 1 Multiplication Learn 3 multiplication properties of exponents.

Exponent Vocabulary an = a • a • a…..a n times Base number: the number being multiplied. a is the base number. Power: the number of times the base is multiplied. n is the power.

The factors of a power, such as 74, can be grouped in different ways The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

Multiplication with the same base: am • an = am+n PRODUCT of POWERS PROPERTY Multiplication with the same base: am • an = am+n Keep base the same and add exponents Use when you are multiplying a power with another power that has the SAME BASE! x5 • x8 = x(5+8) = x13

Multiplying Powers with the Same Base Multiply. Write the product as one power. 1. 66 • 63 2. n5 • n7 6 6 + 3 Add exponents n 5 + 7 Add exponents n 12 6 9 If instructions said ‘Evaluate’ or ‘simplify’: would be to simplify fully =10,077,696 3. 25 • 2 Think: 2 = 2 1 4. z4 • z4 2 5 + 1 z 4 + 4 Add exponents Add exponents 2 6 z 8 If instructions said ‘Evaluate’ or ‘simplify’ =64

Multiplying Powers with the Same Base Simplify: 5. 52 x4 y • 5 x2 y3 5 2+1 x4+2 y1+3 Add exponents with like bases 53x6y4 Simplify fully 125x6y4

Powers of powers with the same base: (am) n = amn POWER of POWERS PROPERTY Powers of powers with the same base: (am) n = amn Keep base same and multiply exponents Use when you are raising an entire power to another power, distribute and multiply the exponents (there are not bases that need to match) (24)6 = 2(4•6) = 224

Powers of a product of different bases POWER of a PRODUCT PROPERTY Powers of a product of different bases (a • b)m = am • bm = ambm distribute power to each base inside and multiply it with existing exponent Use when you are raising an entire expression to a power, distribute and multiply the exponents (there are not bases that need to match) (x4y)6 = x(4•6) y(1•6) = x24y6

Practice! n3  n4 33 • 32 • 35 (-4xy3)3 8 • 88 n7 310 -64x3y9 89

Practice! 3. (32y3)2 4. (5a2b4)5 1. (a • b)4 a4 • b4 a4 b4 2. (-3x)2

3y2(2y)3 (r2st3)2(s4t)3 3y2 23y3 = r4s2t6s12t3 = 3 23y5 = r4s14t9 Some final exponent practice problems… 3y2(2y)3 (r2st3)2(s4t)3 3y2 23y3 = 3 23y5 =24y5 = r4s2t6s12t3 = r4s14t9