- V{2df 2 8. ^256a3
- V( 8 x)2 30. i/r ic? 31. \/625y3
- V36x 33. ^x 3 34.
- Manufacturing A company that manufactures memory chips for digital ^ Se e Pr o b l e m 4.
cameras uses the formula c = 120 ^/n 2 + 1300 to determine the cost c, in dollars,
of producing n chips. How much will it cost to produce 250 chips?
52d 36. Archaeology Carbon-14 is present in all living organisms and decays at a
predictable rate. To estimate the age of an organism, archaeologists measure the amount
of carbon-14 left in its remains. The approximate amount of carbon-14 remaining 3
after 5000 years can be found using the formula A = A 0 (2.7) 5 , where A0 is the initial
amount of carbon-14 in the sample that is tested. How much carbon-14 is left in a sample
that is 5000 years old and originally contained 7.0 X 10-12 grams of carbon-14?
Q Apply Simplify each expression using the properties of exponents, and then write the
expression in radical form.
- (xj)(x^ ) 38. (a i )(a * ) 39. [cd)^[d^)
- (3x5)(8x2) 41. (36x)^(49x)^ 42. (xi)(8x)s
Write each expression in exponential form. Simplify when possible.43 ,^ -^ b 44. 3^^ - 2'v3/o3 45. (x/ab3) - (^ 2 5 6 a 3)- (9x)2 + \J/625y3 47. (^y)(^y)(^y) 48. V(2c)i + ^
- Sp o r t s The radius r of a sphere that has volume Visr= The volume of a
basketball is approximately 434.67 in.3. The radius of a tennis ball is about one
fourth the radius of a basketball. Find the radius of the tennis ball. - a. Show that V x2 = x by rewriting Vx2 in exponential form,
b. Show that \J/x2 = V x by rewriting V x2 in exponential form. - Th i n k ab o u t a Pl an You want to simplify the expression 4x? + 3 Vx3.
- How can you write the radical expression using a rational exponent?
- Can you add the resulting terms?
- What is the result in simplest form?
- Can you write the result in two equivalent forms?
- Open-Ended Write an expression using rational exponents. Then write an
equivalent expression using radicals.
Write each expression in exponential form. See Problem 3.| Lesson 7-5 Rat ional Ex p o nen t s and Radicals 451