Properties Of Exponents
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Properties of Exponents
Multiplying Powers with the Same Base
•am (an) = a m+n •Example: •32 (34) = 36 •x3 (x4) = x7
Raising a Power to a Power
•(an)m = a n(m) •Example: •(34)2 = 38 •(x4)6 = x24
Raising a Product to a Power
•(ab)m = am bm •Example: •(3x)6 = 36 (x6) =729 x6
Dividing Powers with the Same Base
•am /(an) = a m-n •Example: •34 /(32) = 32 •x5 (x2) = x3
Raising a Quotient to a Power
•(a/b)m = am / bm •Example: •(3/4)2 = 32 /42 = 9/16 •(3/x)2 = 32 /x2 = 9/x2
Examples:
• • • • •
5 (5 ) -2 6 5 (5 ) 6 -9 3 (3 ) t2(t7)-2 (3z)4 3
4
Examples:
• • • • •
a /a 2 3 2 /x 2 2 4 /2 (x2/y)3 (n3/n2)2 2
4
Multiplying Powers with the Same Base
•am (an) = a m+n •Example: •32 (34) = 36 •x3 (x4) = x7
Raising a Power to a Power
•(an)m = a n(m) •Example: •(34)2 = 38 •(x4)6 = x24
Raising a Product to a Power
•(ab)m = am bm •Example: •(3x)6 = 36 (x6) =729 x6
Dividing Powers with the Same Base
•am /(an) = a m-n •Example: •34 /(32) = 32 •x5 (x2) = x3
Raising a Quotient to a Power
•(a/b)m = am / bm •Example: •(3/4)2 = 32 /42 = 9/16 •(3/x)2 = 32 /x2 = 9/x2
Examples:
• • • • •
5 (5 ) -2 6 5 (5 ) 6 -9 3 (3 ) t2(t7)-2 (3z)4 3
4
Examples:
• • • • •
a /a 2 3 2 /x 2 2 4 /2 (x2/y)3 (n3/n2)2 2
4
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