1. Which factors of the base would help simplify the expression 1614

(1 point)
Responses

16 = 4*2*2
16 = 4*2*2

16 = 4*4
16 = 4*4

16 = 8*8
16 = 8*8

16 = 2*2*2*2
16 = 2*2*2*2
Question 2
2. Given that the cube root of 27 is 3, what is 2743
?(1 point)
Responses

12
12

108
108

81
81

4
4
Question 3
3. What is the correct simplification of 2532
?(1 point)
Responses

125
125

37.5
37.5

625
625

75
75
Question 4
4. Given that the meaning of the rational exponent can be connected to the meaning of a root, how can you rewrite 35–√
using a rational exponent?(1 point)
Responses

35
3 to the 5th power

51
5 to the 1th power

53
5 cubed

513
5 raised to the 1 third power
Question 5
5. How can you rewrite 812
(1 point)
Responses

8–√
square root of 8

8–√12
1 halfth root of 8

8–√1
1th root of 8

12−−√8

1 answer

Here are the answers to your questions:

Question 1: Which factors of the base would help simplify the expression \( 16^{14} \)?

  • Response: \( 16 = 222*2 \)

Question 2: Given that the cube root of 27 is 3, what is \( 27^{43} \)?

  • Response: \( 108 \) (This is incorrect; the correct answer is \( 27^{43} = (3^3)^{43} = 3^{129} \). In the options given, it might be a typo since it's unclear what the question actually seeks. However, it represents a large exponential instead.)

Question 3: What is the correct simplification of \( 25^{32} \)?

  • Response: \( 625 \) (Since \( 25 = 5^2 \), \( 25^{32} = (5^2)^{32} = 5^{64} = 625 \))

Question 4: Given that the meaning of the rational exponent can be connected to the meaning of a root, how can you rewrite \( 3^{5-\frac{1}{2}} \) using a rational exponent?

  • Response: \( 3^{5} \) (This response is incorrect; the correct way is to combine the exponent: \( 3^{5-\frac{1}{2}} = 3^{4.5} = 3^{\frac{9}{2}} \) but check which was meant by the phrasing.)

Question 5: How can you rewrite \( 8^{\frac{1}{2}} \)?

  • Response: \( 8^{-\frac{1}{2}} \) is often interpreted as the square root of 8, so the answer is square root of 8

If you require further clarity or more questions, feel free to ask!