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Using Properties of Exponents In Exercises 7-10, use the properties of exponents to simplify the expressions.
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Chapter 1 Solutions
EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 4y28y4 (b) z+23z+21arrow_forwardEvaluate or simplify each expression. (2) (a) (b)arrow_forwardDiscrete Math Let a be an odd integer. Show that (a) 8 | a^2 − 9; (b) 16 | a^4 − 81.arrow_forward
- EXAMPLE 1 Simplify each expression. Assume that x can represent any nonzero real number. (a) 64-1/2 (b) (-16)-5/4 (c) -625-3/4 (d) (-32x5)-2/5 and (e) 1 25-3/2 Strategy 1 or x-m/n We will use one of the rules x-m/n 1 xm/n to write the reciprocal of each exponential expression and change the exponent's sign to positive. tm/n Why If we can produce an equivalent expression having a positive rational exponent, we can use the methods of this section to simplify it. Solution 1 Because the exponent is negative, write the reciprocal of 64¬1/2, and change the sign of the 1 (a) 64-1/2 641/2 64 8. exponent. (b) (-16)-5/4 is not a real number because (-16)5/4 is not a real number. (c) In -625-3/4, the base is 1 1 -625- -3/4 625)3 1 1 %3D %3D %D 6253/4 53 125 1 1 (d) (-32x5)-2/5 = 1 %D %D (-32x5)2/5 ¯ (V-32x5)2 (-2x)² 1 (e) -3/2 = 253/2 = (/25)³ = 53 = Because the exponent is negative, write the reciprocal of 1 25-3/2 and change the sign of the 25-3/2' exponent. ||arrow_forwardwhat’s a exponent?arrow_forward-2 What is the value of (3*) -written in standard form? (3)6 9 1 O 3arrow_forward
- ctivity 1: Quotient of Powers 1. Complete the table to explore patterns in the exponents when dividing expressions with exponents. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it. The first two rows are done for you. Expression a. b. C. 210 23 8.25 6x3 15x6 5x2 like x -8m³n7 2m³n 6xy³ d. 15y2 2-2-2-2-2-2-2-2-2-2 2-2-2.27 = 1.27 2-2-2 2-2-2 2-4-x-x-x-x-x 2-3-x-x-x Expanded = = 2-1-2-1 4 2.I-I-I 3 = 2-5-r-r--r-r 2.rrr. 5r² = 1.5² Гарафаф 2.r.r.r x x = 1.r² ● If you chose to skip one entry in the table, which entry did you skip? Why? Math 1. Unit 6. Lesson 2 Student 149 Fewest number of exponents 27 حراب xa x². 2. Use the patterns you found in the table to write as an equivalent expression with a single exponent, लंarrow_forwardEvaluating an Algebraic Expression In Exercises 15-20, evaluate the expression for the given value of x. 7x2,x=4arrow_forwardExpanding an Expression In Exercises 25-38, expand the expression by using Pascal’s Triangle to determine the coefficients. 3v+26arrow_forward
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