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Laws of Exponents x *x x 4 8 12 ( a * b) a * b 3 3 3 3113 315 318 By Chancy Nordick Review What exactly is a power function again? A power function has two parts: y x Review Continued Where x x1 * x2 ........* xn 1 * xn n And b 1 x b x Multiplication Laws What if we want to multiply two power functions? 2 4 Example: x x ( xx)( xxxx) xxxxxx 6 x Multiplication Laws In General a b x x x a b Note: Bases must be the same! a b A few examples x x x a b 4 7 2 *2 2 4 7 2 11 3 x 4 x 3x b *b 4x b b 7x First Law xm*xn = xm+n Notice that the bases have to be the same. Find x2*x3 Find x3y*x4y7 Find z2x5y9*zx7y4 Multiplication Laws Now, what about powers of powers? Example: 2 3 (a ) 2 2 2 a *a *a (aa )(aa )(aa ) 6 a Multiplication Laws In General (x ) x a b ab A few examples (x ) x a b ab 2 2 6 3 3*6 2 18 x x 28 2*8 x16 The Third law (xm)n = xmn Find (x4)5 Find (x3y9)8 Find (2x3y4)3 Multiplication Laws Finally, how do I deal with powers of a product? 3 Example (h * j ) (h * j )(h * j )(h * j ) h*h*h* j * j * j 3 3 h *j Multiplication Laws In General ( xy ) x y a a a Second Law (xy)m = xmym The base does not have to be the same here. Find (xy)7 Find (xy)5 Find (2x)3 Quick Review a b x x x a b (x ) x a b ab ( xy ) x y a a a A few examples (3* x ) 9x 2 2 (ax) (ax ) a x 23 6 6 6 (2t )3 ( t 2 ) 8(t 3 )(t 2 ) 8t 5 4 *2 2 * 2 2 *2 23 x x x 2x x 2x x We’re done…. With the multiplication laws, before We go on…. Stand up and Stretch! Onward! to the division laws Division Laws Example 7 x xxxxxxx 3 xxxx x 4 x xxx Division Laws In General a x a b b x ,x 0 x a A few Examples x a b b x ,x 0 x 8 l 8 6 l 6 l l 2 x 4 3 ( x 4) 4 34 3 3 x The Fourth Law xm/xn = xm-n The base has to be the same. Find x5/x3 Find x3y2/x2y Division Laws Similar to Multiplication 3 h h h h h3 j * * 3 j j j j Division Laws In General a x x a y a ,y0 y a x xa Examples y ya , y 0 3 4 3 4 3 5 5 4 4 x x 7 7 4 Quick Review of Division Laws a x a b b x ,x 0 x a x x a y ya , y 0 Laws of Exponents Compute: 2 5 Answer: 32 Laws of Exponents Compute: 5 -2 Answer: 1/25 Laws of Exponents Compute: 0 2 Answer: 0 Laws of Exponents Compute: 2 0 Answer: 1 Laws of Exponents Compute: 0 0 Answer: ?? Laws of Exponents Compute: - 42 Answer: -16 Laws of Exponents Compute: (-4) 2 Answer: 16 Laws of Exponents Compute: - 4-2 Answer: - 1/16 Laws of Exponents Compute: 0.125 -2 Answer: 64 Laws of Exponents Compute: (4 5 )(42) Answer: 47 or 16,384 Laws of Exponents Compute: (4 5 )2 Answer: 4 10 or 10,485,676 Laws of Exponents What is one-third of 399 ? Answer: 3 98

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posted: | 5/2/2013 |

language: | English |

pages: | 39 |

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