1h4 Exponents date: Remember: never leave negative exponents in your final answers. Exponent rules:

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1 h4 Exponents date: Remember: never leave negative exponents in your final answers. Exponent rules:. x m x n = x m+n when multiplying powers with the same base: keep the base and add the exponents. x m : x n = x m n when dividing powers with the same base: keep the base and subtract the exponents. 3. ( x ) m n = x mn when there is a power to a power: multiply the exponents. 4. ( xy) m = x m y m an exponent acting on a product (multiplying question) acts on each part of the product * rule 3 & 4 used together: ( 3x 3 y ) = ( 3) x 3 y = 9x 6 y 4

2 h4 Exponents date: 5. x y m = xm y m an exponent acting on a quotient (dividing question) acts on each part of the quotient 6. x 0 = Anything to the power of zero is equal to. 7. NEW THIS YEAR: Working with negative exponents. x n = also, = x n A negative exponent is like division. Therefore, x n x n we rewrite it with a positive exponent on the other side of the fraction. Ie. If it was a numerator with a negative exponent, it becomes a denominator with a positive exponent. If it was a denominator with a negative exponent, it becomes a numerator with a negative exponent. From now on, your final answers may never have negative exponents in them. All final answers must be written with positive exponents.

3 h4 Exponents date: Some general guidelines for the order of things when dealing with many rules in the same question:. look for zero exponents first. if possible simplify things inside of brackets 3. power of power: i. move complete brackets up or down if the outside exponent is negative. ii. Then expand power of power by multiplying exponents. Be careful of coefficients 4. next, move single powers with negative exponents up or down and multiply and divide powers with the same base by adding or subtracting exponents. 5. Lastly, make sure that any variables only appear once in the answer and that all exponents are positive. Be careful with negatives. Do not mix up negative numbers, or negative coefficients with negative exponents. For example: 3 is not -6!!! 3 = 3 = 8 also is not!!! is 3

4 h4 Exponents date: A. Simplify using the laws of exponents. Show all steps where appropriate. Final answers must have positive exponents. Be careful (-9x) 0 (-x) 4. ( x ) 3 5. ( abx ) ( 3x 0 y ) 8. ( ) 3 9. ( x ) 3 ( x ) 4 ( x ) 3. ( 5x )( 4 3x 6 y ) 6. ( 3 ) ( x) ( 0x) 0 ( 0x ) 0 3. ( 3x) 3 ( 3x) x 3 m 4 6xm + 4m 4m 7. ( 4x 5 u ) 3 ( xu ) 3 ( 8z 5 u ) 5 3 ( z ) xy +8x y 3 9xy 8. 3xy ( a ) 3 ( a 6 c ) 6 9. x y 7. ( ) 3 x 3 (x 6 y 9 3 ) x ( 3h 6 k ) 4 3h 5 k 3. (( m )( 3 m m )) 4. ( ) 5 9z 3 3z 4 ( xy) x 3 ( ) ( x y) B. Simplify each question fully. ) 4yx 4 x ) x 3 y 3 3xy 4 x y 3 3) x 4 y 4 y 4 4) x y 3 y (3b 0 ) 4 (x y 3 ) 4 7) (yx 4 ) (4v ) 9) m m 4 m n 3 3nm 0) x 3 y 4 y 0 3y 4 ) 4x 3 y x y 3xy 3 ) m 3 4nm 4 m n

5 h4 Exponents date: 5 C. Simplify each question fully. h4 Exponents d x 0 y 4 xy 4 er ML3LMCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l nswer should contain only positive exponents. )3 ) 4 4) ( ( y 3 ) 0 ( x y ) y ) 0 4 ) 4 Simplify. Your answer should contain only positive exponent ) ( v u v 4) ( ( y 3 ) x ( x 3 y 4 ( x ( x ) 0) x 3 y ( 4 3 e Date y ) )3 y ) mer ML3LMCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l answer should contain only positive exponents. )3 n ) 4 4) ( ( y 3 ) 0 ( x y ) y ) ) 0 4 ) 4 ) Simplify. Your answer should contain only positive exponen ) ( v u 4) ( ( y ( x 3 y ( ( x ) 0) x 3 ) ( y 3 ( e Date y ) y 3 y ) y 3 ML3LMCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l nswer should contain only positive exponents. 3 ) 4 4) ( ( y 3 ) 0 ( x y ) y ) ) 4 ) 3 y 3 N Simplify. Your answer should contain only positive expon ) ( 4) ( ( ( x ( ( x 0) x ) ( y x y 3 x 0 ( m e Date y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4 y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4 MCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l wer should contain only positive exponents. 4 4) ( ( y 3 ) 0 ( x y ) y ) ) y 3 (m 4 n 4 ) 4 m n 4 m 4 N Simplify. Your answer should contain only positive expon ) ( 4) ( ( ( x ( ( x 0) x ) ( y x y 3 x 0 ( m e Date y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4 y ) 9) x 0 y 4 xy LMCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l swer should contain only positive exponents. 4 4) ( ( y 3 ) 0 ( x y ) y ) 3 e_ u v 3 4) ( ( y 3 )0 ( x ( x 3 y 4 ( x 4 ) ( x ) 0) x 3 y 3 ( x e y ) y ) 3LMCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l swer should contain only positive exponents. ) 4 4) ( ( y 3 ) 0 ( x y ) y ) ) e Simplify. Your answer should contain only positive exponents ) ( v u v 3 4) ( ( y 3 )0 x ( x 3 y 4 ( x 4 ( x ) 0) x 3 y ( x y 3 (x e y ) y 3 y ) y 3 MCF.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l wer should contain only positive exponents. 4 4) ( ( y 3 ) 0 ( x y ) y ) y 3 Simplify. Your answer should contain only positive exponen ) ( v u 4) ( ( y ( x 3 y ( ( x ) 0) x 3 ) ( y 3 ( x y 3 x 0 (m m n e y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4 y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4.0 y 8A6lglF ArpiEgRhotUs8 ErOecsHetryvUeCdi.l er should contain only positive exponents. 4) ( ( y 3 ) 0 ( x y ) y ) y 3 (m 4 n 4 ) 4 m n 4 m 4 Simplify. Your answer should contain only positive exponen ) ( v u 4) ( ( y ( x 3 y ( ( x ) 0) x 3 ) ( y 3 ( x y 3 x 0 (m m n e y ) y 3 x y 3 x 0 (m 4 n 4 ) 4 m n 4 m 4

6 h4 Exponents date: Answers: A.. 6x y 4. 3x 4 3. x 4. 8x 6 5. a b x y x 8. 5y 6 x. 40x 3. 43x x 4 u xy 3y 56z x 3 m 3 + 4x u 5 a 5 c 9. 4y h 7 k 5. 04z x 4 9. y 3 x x 3 y 3 B. ) 4yx 5 ) 6x y 3) 8x 8 y 3 4) x y 7) y x x 8 y v 9) 4m0 0) y8 x 3 4y n ) ) 3n 4 3 3x 6 8m 3 3) m 7 n 4 4a v 6 u 3 u 7) 8x y 3 y 0 9) a3 0) b a 3 b 4 ) v0 4u 6 ) 8y x 4 3) y 8x 9 y 9 8 7) x 6 y 7 4u v 4 4) 6y x 8 x 8y 7 C. ) y ) u4 v 8 x 56 y x 3 x 0 y 3 3) m5 6n 6 u 0 v 8 4) 8y3 x 5 8x y 9) 6x 0) y ) 8x 4 y 6 ) x9 3) 8x y 6 4y4 x x0 y 3 y 9 3m n 0 6