Expl an ation : An expression raised to a power raised to another power is equivalent to the expression raised to the product of the powers.

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1 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing Analytic Geometry (CCGPS) EOCT Quiz Answer Key Number and Quantity - (MCC9 2.N.RN.. ) Rational Exponents, (MCC9 2.N.RN.2 ) Properties Of Exponents, (MCC9 2.N.CN. ) Complex Number Definition, (MCC9 2.N.CN.2 ) Complex Number Arithmetic, (MCC9 2.N.CN.7 ) Solve Quadratic Equations Student Name: Teacher Name: Micah Shue ) Use the properties of exponents to solve the equation ( / ) x =. A) x = B) x = Date: Score: x = x = An expression raised to a power raised to another power is equivalent to the expression raised to the product of the powers. Therefore, ( / ) x = x. In order for the answer to be the same as the base in the original expression, x must be equal to one. This would only be true if and x are reciprocals. Therefore, x = 2 ) Use the properties of exponents to simplify the expression. A) 2 B) 2 = - = - = 2 = 2 /8

2 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing ) Which expression is equivalent to 2a 2 b / c? A) 0a 0 b c 2 B) 0a 0 b c 2 2 a 0 b c 2 2a 0 b c 2 2 is the fifth root of , a 2 is the fifth root of a (2)(), b / is the fifth root of b (/)(), and c is the fifth root of c ()(). Therefore, 2 is the fifth root of 2, a 2 is the fifth root of a 0, b / is the fifth root of b, and c is the fifth root of c 2, so 2a 2 b / c = 2 a 0 b c 2. 4 ) Which expression is equivalent to 64x 6 y 4 z? A) B) 6x 2 y 4 x 2 y 4x y x2 y z z 4 z 64x 6 y 4 z = 64 (x 6 ) / (z ) /. Since the number that when multiplied by itself twice equals 64 is 4, and since (x m ) n = x mn, the expression can be further simplified as follows: 64 (x 6 ) / (y 4 ) / (z ) (/) = 4 x (6)(/) y (4)(/) z ()(/) = 4 x 2 y 4/ z = 4 x 2 y 4/ z. ) Wh ich equation justifies wh y 2 7 A) = 2 7 B) 2 7 (2 7 (2 7 = ) = 2 7 ) = ( ) is equival an t to th e cube root of 2 7? We wan t 2 7 ) = (2 7 ) to h ol d true so th at (2 7 ) = /8

3 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing 6 ) Iden tify th e radical expression of /. A) / B) / / is correct. The radical expression for th e expression / is. 7 ) Simpl ify th e expression. A) 9 B) 9 xy 9 x 2 y 2 9 x 2 y 2 9 x 2 y 2 is correct. Usin g th e rul e for dividin g powers, we get xy - in th e paren th eses, wh cih th en becomes x y, usin g th e n egative expon en t rul e. Fin al l y, square to get th e an swer. 8 ) Simpl ify th e expression. A) 9 vw 4 B) 9 v 2 w 9 v w 4 9 w 4 v 9 vw 4 is correct. Raisin g each item to th e power -2 resul ts in a fraction with w 4 in th e n umerator an d - 2 v - in th e den omin ator. Movin g th e den omin ator items up to th e n umerator makes th eir powers positive an d gets th e an swer. /8

4 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing 9 ) Wh ich expression is equival en t to m 4/ 2 r / 2 in simpl ified form? A) m 4 r B) mr m 2 r m 2 r r Rewrite as perfect squares an d th en simpl ify so m pair can be pulled out from under a radical and simplified. 4 2 r 2 = m 4 r = m 4 r 2 r = m 2 rr. Remember anything that is a 0 ) Complex numbers are written in the form a + bi. What does i represent? A) - B) - i = - 4/8

5 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing ) Which point graphed here is 2 + i? A) B) The point for 2 + i is (2,). The correct answer is B. /8

6 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing 2 ) What is the CONJUGATE of the complex number that is graphed? A) -2 + i B) - 2i -2 - i 2 - i The point that is graphed is -2 + i. The conjugate just changes the middle sign. The correct answer is -2 - i. 6/8

7 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing ) Which is equivalent to i 224? A) - B) 0 i Remember that all powers of i can be reduced. i = i i 2 = - i = -i i 4 = Therefore i 2 24 = 4 ) Express in terms of i: A) -2 4 i B) -24 i 24i 24 i A negative under the radical can be pulled out and becomes i. So = -i 64 = -i(8) = -2 4 i. ) Simplify the expression. A) -4 B) 2i 2i 2 4 ( -4 ) = 2i (2i)(2i) = 4i 2 = -4 ( -4 )( -4 ) 6 ) Perform the indicated operation. (-9 + 2i) - (-2 + 4i) = A) -2-6i B) - + 6i - 2 i 2 + 2i (-9 + 2i) - (-2 + 4i) = (-9 + 2) + (2-4)i = - 2 i 7/8

8 4/2/204 USATestprep, Inc. - Online State-Specific Review and Benchmark Testing 7 ) Simplify the expression. A) - B) i 4 + 9i - 2i (2 + i) i is correct. Use FOIL to expand the binomial, which becomes 4 + 2i + 9i 2. This simplifies to 4 + 2i ) Solve. A) x = 2 B) x = 2i x = ±2 x = ±2 i x = 0 Subtract four from both sides and then you have x 2 = -4 this is going to cause a complex number. The solution is x = ±2 i 9 ) Find all complex solutions for the equation x 2 = 4x A) {-2, 2i} B) {-i, i} {2 - i, 2 + i} {7 - i, 7 + i} {2 - i, 2 + i} Since the equation is not factorable, use the quadratic formula with a =, b = -4, and c = ) Find all solutions to x 2 + 2x + = 0 A) - and 2 B) no solution - ± 2 - ± 2 i The correct answer is - ± 2 indicating a complex number. i. If you use the quadratic formula a =, b = 2 and c =. You get a negative under the radical 2 ) The solution set for the equation x 2-6x + 0 = 0 is A) {-2i, i} B) { - i, + i} { - i 9, + i 9 } {-2 - i, -2 + i } { - i, + i} is correct. Use the quadratic formula. 8/8