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#1: To evaluate this expression, we use PEMDAS (parenthesis, exponent, multiplication, division, addition, subtraction, in that order.)

#2: Both 24 × c and 24c represent the total number of water bottles.

#3: To do this one, we plug in 18 into each equation and solve them.

3a:

3b:

3c:

3d:

3e:

With this information, we can conclude that expressions 2, 4, and 5 equal 24 when x = 18.

#4: Though both expressions contain the same number, their value is different.

5² = 5 × 5 = 25

2⁵ = 2 × 2 × 2 × 2 × 2 = 32

This shows that even though the same numbers are used, the answer is different because they are raised to different powers.

#5:

To solve these, we use the distributive property and we find that all but the second expression are equivalent.

5a. 3(3a + 4) = 6a + 12          Yes

5b. 3(5b - 2) ≠ 8b - 5             No

5c. 5(5c + 6) = 30 + 25c       Yes

5d. 4(5d - 4) = 20d - 16         Yes

#6: To find that out, we find the Greatest Common Factor (or GCF) of each pair of numbers.

GCF of 15 and 25 = 5

GCF of 40 and 70 = 10

GCF of 45, and 60 = 15

GCF of 65 and 75 = 5

The only pairs of numbers with a GCF of 5 are 15, 25 and 65, 75.

Hope this helps!

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step-by-step explanation: