Precalc0001to0005-page24

Precalc0001to0005-page24 - . 5 x y n = x n y n The power of...

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(Section 0.5: Exponents and Radicals: Laws and Forms) 0.5.2 If m and n are positive integers (not both even; see Footnote 1), x m / n can be written as x m n or as x n () m . For example, x 3/5 can be written as x 3 5 or as x 5 () 3 . PART C: LAWS OF EXPONENTS AND RADICALS The term power usually refers to an exponent . However, we often refer to x n as a power of x . Laws of Exponents If the expressions involved are real -valued, then the following laws apply. # Law In Plain English / Comments 1 x m x n = x m + n To multiply powers of x , add the exponents. For example, x 2 x 3 = xx () xxx () = x 5 . 2 x m x n = x m ± n To divide powers of x , subtract the exponents. 3 x m () n = x mn To raise a power to a power , multiply the exponents. 4 xy () n = x n y n The power of a product is the product of the powers
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Unformatted text preview: . 5 x y n = x n y n The power of a quotient is the quotient of the powers . 6 x = 1 This is consistent with Law 2, with m = n . (We define to be 1 here. See Section 1.3, Part H.) 7 1 x n = x n This is consistent with Laws 2 and 6. 8 x y n = y x n x y 1 = 1 x y = y x y ( ) . Use Law 3 with m = 1 . WARNING 1 : These laws may or may not apply when the expressions involved are not real-valued; 2 ( ) 1/ 2 , for example, cannot be defined as a real value. Also, we require nonzero denominators in Laws 2, 5, 7, and 8....
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This document was uploaded on 12/29/2011.

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