CHAPTER 7 REVIEW. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Name: lass: ate: I: HPTER 7 REVIEW Multiple hoice Identify the choice that best completes the statement or answers the question.. The head of a pin is m wide. Simplify 0 5. a b c d Simplify (.4 0 ) (4 0 6 ) and write the answer in scientific notation. a b. 3 c d Simplify ( 5). a. 5 b. c. d Simplify 3 0. a. b. 3 c. 0 d Evaluate a b 0 for a = 3 and b =. a. 9 b. c. d x 8 3 Ê ˆ. Simplify. x 4 y 6 x 64 x a. b. c. d. y 8 x 7 8 y y 9 Ê 3 3. Simplify 5 ˆ. a. 5 b. 5 c. 9 d x y 8 5. Simplify 6w0 r 8 t 6. a. 6r 8 t 6 b. 6wr8 t 6 c. 6t6 r 8 d. 6 r 8 t 6 6. Find the value of the power 0 8. a b. 80 c d Write 0.0 as a power of 0. a. 0 b. 0 c. 0 d Find the value of the expression a. 3,600 b. 7,00,000 c. 7,000,000 d. 70, Simplify ( ) 4 ( ) 4. a. 56 b. 6 c. 56 d. annot simplify 4. Simplify the expression a. 4 b. 8 c. 5 d Simplify the expression 3 a. b. c. 9 d Write the polynomial x 3 6x + 7x 4 + 7x 4x 5 0 in standard form. Then give the leading coefficient. a. 4x 5 + 7x 4 + 7x 3 x 6x 0 The leading coefficient is 4. b. 0 6x + 7x + 7x 3 x 4 4x 5 The leading coefficient is 0. c. 4x 5 + 7x 4 x 3 + 7x 6x 0 The leading coefficient is 4. d. 0 6x + 7x x 3 + 7x 4 4x 5 The leading coefficient is Simplify a. 390,65 b. annot simplify c. 5 d..6

2 Name: I: 7. lassify the polynomial according to its degree and number of terms. 5x 3 y + 6x y + 9y 7x + 8 a. The polynomial is a quartic polynomial. b. The polynomial is a quintic trinomial. c. The polynomial is a quadratic trinomial. d. The polynomial is a quadratic polynomial. 8. Tell whether the number 9 is a root of 3r r 45. a. No b. Yes 9. Tell whether the number 5 is a root of 4r r 49. a. Yes b. No 0. dd or subtract. t 5t 3 + 9t 0t 3 a. 4t 4 b. t 5t 6 c. t 5t 3 d. 7t+ 5t 3. dd. (3c 4 c ) + (c 4 + 6c ) a. 4c 4 + 5c b. 4c 8 + 5c 4 c. 4c 4 + 5c d. 3c 4 + 6c. Subtract. (9c 3 c ) (c 3 + 7c 4) a. 8c 3 8c b. 9c 3 + 7c 4 c. 9c 3 8c 4 d. 8c 3 8c Multiply. r 4 s 3Ê 4r 5 r 3 s 3 ˆ a. r 0 s 4 + r 8 s 7 b. 8r 0 r s 9 c. r 9 s 3 + r 7 s 6 d. 8r 9 s 3 r 7 s 6 4. Simplify n 9 m n 7. a. n 6 m b. (n m) 4 c. n m d. n 63 m 5. Multiply. (x 4)(x 3) a. x(x 3) 4(x 3) b. x 4x + c. x 7x + d. x + 6. Multiply. ( 5x 3)(x 3 5x + ) a. 5x 4 3x 3 + 5x 5x 6 b. 5x 4 3x 3 5x + 5x 6 c. 5x 3 8x + 5x 6 d. 5x 3 + x 5x 6 7. Multiply. (4x + 5y ) a. 6x + 0x y + 5y b. 8x + 0y c. 6x + 5y d. 6x + 40x y + 5y 8. Multiply. (z 5) a. z 0z 5 b. z 0z 5 c. z + 0z + 5 d. z 0z Multiply. (r + 3)(r 3) a. r + 6 b. r 6 c. r 9 d. r 3r Simplify. ll variables represent nonnegative numbers. 8 Ê ˆ a 4 b b a. a b 9 b. a 4 b 5 c. a 3 b 4 d. a 3 b 5

3 I: HPTER 7 REVIEW nswer Section MULTIPLE HOIE. NS: 0 5 = 0 5 = heck the exponent. The exponent is negative. heck the exponent. REF: Page 395 TOP: 7- Integer Exponents KEY: negative exponent power exponent. NS: ( 5) = ( 5) The reciprocal of 5 is ( 5) = 5 ( 5) = 5. nonzero number raised to a negative exponent is equal to divided by that number raised to the opposite (positive) exponent. heck the sign of your answer. negative exponent does not affect the sign of the answer. nonzero number raised to a negative exponent is equal to divided by that number raised to the opposite (positive) exponent. REF: Page 395 TOP: 7- Integer Exponents KEY: negative exponent evaluate power exponent

4 I: 3. NS: ny nonzero base to the zero power is equal to. 3 0 = nonzero number raised to the zero power is equal to. nonzero number raised to the zero power is equal to. nonzero number raised to the zero power is equal to. REF: Page 395 TOP: 7- Integer Exponents KEY: zero exponent zero power evaluate power exponent 4. NS: a b 0 ( 3) ( ) 0 Substitute 3 for a and for b. ( )() 9 Evaluate expressions with exponents. 9 Simplify. nonzero number raised to a negative exponent is equal to divided by that number raised to the opposite (positive) exponent. ny nonzero number raised to the zero power is. ny nonzero number raised to the zero power is. REF: Page 395 TOP: 7- Integer Exponents KEY: zero exponent zero power evaluate power exponent

5 I: 5. NS: 6w 0 r 8 t 6 = 6 r 8 t 6 = 6 r 8 t 6 = 6 r 8 t6 t 6 = t6. = 6t6 r 8 Rewrite 6w 0 r 8 without negative or zero t 6 exponents. Simplify each part of the expression. r 8 = r. 8 ny number to the zero power is equal to. negative exponent in the numerator becomes positive in the denominator. ny number to the zero power is equal to. negative exponent in the numerator becomes positive in the denominator. negative exponent in the denominator becomes positive in the numerator. REF: Page 396 TOP: 7- Integer Exponents KEY: exponent negative exponent simplify 6. NS: Start with and move the decimal point eight places to the right. 0 8 = Start with and move the decimal point. If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. ount the number of places to move the decimal point. REF: Page 400 TOP: 7- Powers of 0 and Scientific Notation 3

6 I: 7. NS: The decimal point is places to the left of, so the exponent is. 0.0 = 0 The number is less than one, so the exponent is negative. ount the number of decimal places to the left of. The exponent is the opposite of that number. ount the number of decimal places to the left of. The exponent is the opposite of that number. REF: Page 40 TOP: 7- Powers of 0 and Scientific Notation KEY: write exponents power powers of 0 8. NS: Move the decimal point 5 places to the right. 7,00,000 For powers of 0, the exponent tells the number of places to move the decimal point. Move the decimal point the correct number of places. Move the decimal point the correct number of places. REF: Page 40 TOP: 7- Powers of 0 and Scientific Notation KEY: exponents multiplication power powers of 0 9. NS: To multiply powers with the same base, keep the same base and add the exponents. Then, evaluate the power. ( ) 4 ( ) 4 = ( ) 8 = 56 heck the sign of the exponent. The exponent tells how many times to multiply the base number by itself. If the bases are the same, add the exponents. Then evaluate the power. REF: Page 409 TOP: 7-3 Multiplication Properties of Exponents KEY: evaluate product multiply power exponent 4

7 I: 0. NS: To divide powers with the same base, keep the same base and subtract the exponents. To divide powers with the same base, subtract the exponents. The bases are the same, so the expression can be simplified. To divide powers with the same base, subtract the exponents. REF: Page 45 TOP: 7-4 ivision Properties of Exponents KEY: exponent power division base. NS: Write as a product of quotients: Simplify each quotient to get If necessary, adjust the result so it is in scientific notation with exactly one digit to the left of the decimal point. Write your answer in scientific notation. heck the exponent. heck the exponent. REF: Page 46 TOP: 7-4 ivision Properties of Exponents 5

8 I:. NS: 4x 8 3 Ê ˆ x 4 y 6 = = = Ê 4x 4 y 6 Ê 4x 4 Ê y 6 ˆ 3 ˆ 3 Simplify exponents with like bases: x 8 x = x 4. 4 Use the Power of a Quotient Property. 3 ˆ ( 4) 3 (x 4 ) 3 Use the Power of a Product Property. (y 6 ) 3 = (64)(x 4 ) 3 (y 6 ) 3 Simplify: ( 4) 3 = x = y 8 Use the Power of a Power Property to simplify the exponents. Use the Power of a Power Property to raise the constant to the power outside the parenthesis. heck to see if the terms are correctly placed in the numerator and denominator. Use the Power of a Power Property to raise every term in the problem to the exponent outside the parenthesis. REF: Page NS: Ê 3 5 ˆ Ê 5 = 3 ˆ 5 = TOP: 7-4 ivision Properties of Exponents Rewrite with a positive exponent. Use the Power of a Quotient Property, and simplify. First, rewrite the fraction with a positive exponent. Then, use the Power of a Quotient Property and simplify. When you rewrite the fraction with a positive exponent, the numerator and the denominator switch places. Raising a fraction to an exponent is different from multiplying the fraction. REF: Page 48 TOP: 7-4 ivision Properties of Exponents 6

9 I: 4. NS: = 6 = = = Use the definition of b n. number raised to the power of /n is equal to the nth root of that number. Rewrite the denominators of the powers as roots. number raised to the power of /n is equal to the nth root of that number. REF: Page 4 TOP: 7-5 Fractional Exponents KEY: fractional exponent 5. NS: 3 5 Ê = 5 ˆ 3 Ê ˆ = 5 5 = ( ) = 4 efinition of b m n. number raised to the power of m/n is equal to the nth root of the number raised to the mth power. Rewrite the denominator of the power as a root. Rewrite the base as a number raised to a power. REF: Page 43 TOP: 7-5 Fractional Exponents KEY: fractional exponent 6. NS: The standard form is written with the terms in order from highest to lowest degree. Find the correct coefficient of the x-cubed term. The standard form is written with the terms in order from highest to lowest degree. The standard form is written with the terms in order from highest to lowest degree. REF: Page 43 TOP: 7-6 Polynomials KEY: polynomial 7

10 I: 7. NS: polynomial that has a highest degree of 4 is called a quartic polynomial. polynomial with 5 terms is called simply a polynomial. heck the highest degree and the number of terms. heck the highest degree and the number of terms. heck the highest degree. REF: Page 43 TOP: 7-6 Polynomials KEY: polynomial 8. NS: 3r r 45 = 3(9) (9) 45 Substitute for r. = Simplify. = 0 Yes! 9 is a root of 3r r 45. root of a polynomial in one variable is a value of the variable for which the polynomial is equal to 0. REF: Page 43 TOP: 7-6 Polynomials KEY: polynomial 9. NS: 4r r 49 = 4(5) (5) 49 Substitute for r. = Simplify. = 54 No! 54 0, so 5 is not a root of 4r r 49. root of a polynomial in one variable is a value of the variable for which the polynomial is equal to 0. REF: Page 43 TOP: 7-6 Polynomials KEY: polynomial 8

11 I: 0. NS: t 5t 3 + 9t 0t 3 = t 5t 3 + 9t Identify like terms. 0t 3 = t + 9t 5t 3 Use the ommutative Property to 0t 3 move like terms together. = t 5t 3 ombine like terms. Only add or subtract coefficients on like terms. When combining like terms, only add or subtract the coefficients. The powers stay the same. heck your addition and subtraction. REF: Page 438 TOP: 7-7 dding and Subtracting Polynomials KEY: monomial. NS: (3c 4 c ) + (c 4 + 6c ) = (3c 4 + 6c ) + ( c + c 4 ) + ( ) = 4c 4 + 5c ombine like terms. Identify like terms. Rearrange terms to get like terms together. heck that you have included all the terms. When adding polynomials, keep the same exponents. First, identify the like terms and rearrange these terms so they are together. Then, combine the like terms. REF: Page 439 KEY: polynomial TOP: 7-7 dding and Subtracting Polynomials 9

12 I:. NS: (9c 3 c ) (c 3 + 7c 4) = (9c 3 c ) + ( c 3 7c + 4) Rewrite subtraction as addition of the opposite. = (9c 3 c 3 ) + ( c 7c ) + ( 4) = 8c 3 8c + 4 ombine like terms. Identify like terms. Rearrange terms to get like terms together. heck that you have included all the terms. First, rewrite the subtraction as an addition of the opposite. Then, combine the like terms. heck the coefficients and the signs. REF: Page 439 TOP: 7-7 dding and Subtracting Polynomials KEY: polynomial 3. NS: Use the istributive Property to multiply the monomial by each term inside the parentheses. Group terms to get like bases together, and then multiply. on't forget to multiply the coefficients for each term. When multiplying like bases, add the exponents. Multiply the coefficients for each term; don't add. REF: Page 446 TOP: 7-8 Multiplying Polynomials KEY: polynomial multiplication 4. NS: To multiply powers with the same base, keep the same base and add the exponents. n 9 m n 7 = (n 9 n 7 ) m = n m To multiply powers with the same base, add the exponents, not subtract. Rewrite only powers with the same base. o not combine powers with different bases. To multiply powers with the same base, add the exponents, not multiply. REF: Page 409 TOP: 7-3 Multiplication Properties of Exponents KEY: evaluate product multiply power exponent 0

13 I: 5. NS: (x 4)(x 3) Use FOIL. x(x 3) 4(x 3) istribute x and 4. x(x) + x( 3) 4(x) 4( 3) istribute x and 4 again. x 3x 4x + Multiply. x 7x + ombine like-terms. istribute again, multiply and combine like-terms. You did not multiply the outer terms. You did not multiply the inner and outer terms. REF: Page 448 TOP: 7-8 Multiplying Polynomials KEY: binomial multiplication 6. NS: ( 5x 3)(x 5x + ) 5x(x 3 5x + ) 3(x 3 5x + ) istribute 5x and 3. 5x(x 3 ) + 5x( 5x) + 5x( ) 3(x 3 ) 3( 5x) 3( ) istribute 5x and 3 again. 5x 4 5x + 0x 3x 3 + 5x 6 Multiply. 5x 4 3x 3 5x + 5x 6 ombine like terms. heck the signs. ombine only like terms. ombine only like terms. REF: Page 449 TOP: 7-8 Multiplying Polynomials

14 I: 7. NS: Method ( a + b) = a + ab + b The factors fit the pattern for squaring a binomial to get a perfect square trinomial. Use the rule for ( a + b). a = 4x and b = 5y a = 6x ab = 40x y b = 5y ( a + b) = a + ab + b Identify a and b from the given binomial. Use these values to determine a, ab, and b. Substitute the terms into the corresponding places. (4x + 5y ) = 6x + 40x y + 5y Method (4x + 5y ) = (4x + 5y )(4x + 5y ) Use FOIL to multiply the binomials. = 6x + 0x y + 0x y + 5y = 6x + 40x y + 5y heck your multiplication and addition. Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule for squaring a binomial. Rewrite the binomial square as a product of two binomials. Either use FOIL or the rule for squaring a binomial. REF: Page 455 TOP: 7-9 Special Products of inomials KEY: binomial multiplication

15 I: 8. NS: (z 5) ( a b) = a ab + b Use the rule for ( a b). (z 5) = z (z)(5) + 5 Use the FOIL method, and then combine like terms. z 0z + 5 Simplify. heck the signs. The last term in the product should be the square of the second term in the binomial. heck the signs. REF: Page 456 TOP: 7-9 Special Products of inomials KEY: binomial multiplication 9. NS: (r + 3)(r 3) ( a + b) ( a b) = a b Use the rule for ( a + b) ( a b). (r + 3)(r 3) = r 3 Use the FOIL method, and then combine like terms. r 9 Simplify. The terms in the product should be squares. Use the FOIL method. First, use the FOIL method. Then, combine the like terms. REF: Page 457 TOP: 7-9 Special Products of inomials KEY: binomial multiplication 3

16 I: 30. NS: 8 Ê ˆ a 4 b Ê b = a 4 b ˆ 8 b b = b Ê = Ê ˆ a 4 8 ˆ 8 b b Power of a Product Property = Ê a 3 ˆ Ê b 4 ˆ b Simplify the exponents. = a 3 b 4 + Product of Powers Property = a 3 b 5 Use the Power of a Product Property. istribute the power outside the parentheses to all powers inside the parentheses. The nth root of b raised to the nth power is b. REF: Page 44 TOP: 7-5 Fractional Exponents KEY: fractional exponent 4