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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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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- OA 5 = (3-1) 63 - (2) OB | ABarrow_forwardwhat’s a exponent?arrow_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_forwardEXAMPLE 4 Simplifying Expressions with Exponents Simplify: (a) (2a'b?)(3ab*)³ (b) COLUT IONarrow_forward
- nit 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_forwardEXAMPLE 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_forwardHow to do it in radical formarrow_forward
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