Concept explainers
Using Properties of Exponents In Exercises 7-10, use the properties of exponents to simplify the expressions.
(a)
(b)
(c)
(d)
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Calculus: Early Transcendental Functions (MindTap Course List)
- K Simplify x X 1 2 1 1 2 (2x+5)+ 6x by factoring out x + - 2 (2x + 5) + 6x 1 (Simplify your answer. Type your answer using exponential notation. Use i expression.)arrow_forwardCompute the results. Leave your answers in scientific notation. (5 × 104)(8 × 105) 4 × 106 (10 × 10−5)(9 × 106) 5 × 109arrow_forwardEXAMPI E 7 Simplify each expression. Assume that all variables represent positive real numbers. Write all answers using positive exponents only. a8/3a1/3 a? (a) 52/753/7 (b) (52/7)3 (c) (a2/363/2,6 (d) Strategy We will use the product, power, and quotient rules for exponents to simplify each expression. Why The familiar rules for exponents are valid for rational exponents. Solution (a) 52/753/7 = 52/7 + 3/7 Use the rule xmx" = xm + n. 2 3 5 = 55/7 Add: 7 (b) (52/7)3 = 5(2/7)(3) Use the rule (xm)" = xmn. = 56/7 Multiply: 극(3)-극(클) -윽 (c) (a2/3b1/2)6 = (a2/3)6(b1/2)6 = a12/366/2 Use the rule (xy)" = x^y^. Use the rule (xm)" = xmn twice. Simplify the exponents. a8/3a1/3 a? Use the rules xmx" = xm + n ut - n (d) a8/3 + 1/3 – 2 and %3D = a8/3 + 1/3 – 6/3 2 = 3 8 3 = a3/3 1 + 3 %D 3 3 3 = 1. 3arrow_forward
- Can Please Answer Thanks❤️arrow_forwardctivity 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_forwardnit 5- Polynomials A-APR.1 missions until Wednesday, April 28, 2021 at 3:30 pm Question 3 (1 point) Simplify. (5n + 4n? – 7)- (8n – 6+ 7n) Answer = (use " for exponents, shift-6) Blank 1: Ouectiarrow_forward
- Rewriting with Positive Exponents In Exercises 27-30, rewrite each expression with positive exponents. Simplify, if possible. (a) 4y28y4 (b) z+23z+21arrow_forwardWhat are the three uses of the “-” sign in algebra? Explain how they differ.arrow_forward(a) Explain the meaning of the exponent in the expression 23 . (b) Explain the meaning of the exponent in the expression 23 .arrow_forward
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