Which factors of the base would help simplify the expression 1614?(1 point)
Responses
16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2
16=8⋅8
16 equals 8 times 8
16=4⋅2⋅2
16 equals 4 times 2 times 2
16=4⋅4
16 equals 4 times 4
Given that the cube root of 27 is 3, what is 2743
?(1 point)
Responses
81
81
108
108
4
4
12
81
What is the correct simplification of 2532?(1 point)
Responses
75
75
37.5
37.5
625
625
125
625
Given that the meaning of a rational exponent can be connected to the meaning of a root, how can you rewrite 5–√3 using a rational exponent?(1 point)
Responses
5^3
5 cubed
5^1
5 superscript 1 baseline
3^5
3 superscript 5 baseline
5^1/3
5 superscript Start Fraction 1 over 3 End Fraction baseline
5^1/3
How can you rewrite 8^1/2 using a root?(1 point)
Responses
1/2−−√8
root index 8 Start Root Start Fraction 1 over 2 End Fraction End Root
8–√
Start Root 8 End Root
8–√1/2
root index Start Fraction 1 over 2 End Fraction Start Root 8 End Root
8–√1
Start Root 8 End Root
In order to simplify the expression 1614 using the factors of the base, we need to find the prime factorization of 1614. To do this, we can start by dividing 1614 by the smallest prime number, which is 2.
First, we divide 1614 by 2:
1614 ÷ 2 = 807
Since 807 is not divisible by 2, we move on to the next prime number, which is 3.
Next, we divide 807 by 3:
807 ÷ 3 = 269
Now, we try dividing 269 by 3 again, but since it is not divisible, we move on to the next prime, which is 5.
Dividing 269 by 5:
269 ÷ 5 = 53
Finally, we reach a prime number, which is 53. Since 53 is already prime, we stop.
To summarize the prime factorization of 1614:
1614 = 2 × 3 × 269
Therefore, the factors of the base that help simplify the expression 1614 are 2, 3, and 269.