-36כל הזכויות שמורות - אתי עוזרי & יצחק שלו - מתמטיקה לכיתה ט' - סדרת מעוף - אין לשכפל ללא אישור בכתב מהמחברים © 67 6 7 חשבו את התרגילים הבאים בדרך הפשוטה ביותר ללא שימוש במחשבון. (היעזרו בתרגיל הקודם.) .ג 42 21 5 5 .א 2 5 4 4 ⋅ .ד 360 120 3 3 .ב 4 25 3 3 ⋅ סיכום הפרק (חזקה של מכפלה ושל מנה) y y (a · b)n = an · bn הסבר: למשל: דוגמאות א.. (3·7)4 = 34 · 74 ב.. (23 · 34)5 = (23)5 · (34)5 = 23 · 5 · 34 · 5 = 215 · 320 y y ( ) (b ≠ 0) = a b a b n n n הסבר: למשל: דוגמאות ג.. ( ) = 4 5 4 5 3 3 3 ד.. ( ) = = a b (a ) (b ) a b 2 3 5 2 5 3 5 10 15 (a b) ab ab ab ... ab a a a ... a b b b ... b a b n n n ⋅ = ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ פעמים n פעמים n פעמים n (2 3) (2 3) (2 3) (2 3) (2 3) 2 3 2 3 2 3 2 3 2 2 2 2 3 3 3 3 2 3 4 4 4 ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ פעמים 4 פעמים 4 פעמים n פעמים n פעמים n ... a b a b a b a b a b a a a ... a b b b ... b a b n n n ( ) = ⋅ ⋅ ⋅ ⋅ = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 2 2 2 3 3 3 3 2 3 4 4 4 ( ) ( ) ( ) ( ) ( ) = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
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