Question

41 the volume of a cardboard box with equal sides 5 inches long is $5^3$ cubic inches. which of the following is equal to $5^3$?
a 15
b 75
c 125
d 243

42 a chain letter is sent to four people. each of those people is asked to send the letter the next day to another 4 people. if the chain is not broken for five days, $4^5$ letters will be sent. which of the following is equal to $4^5$?
a 1,024
b 625
c 256
d 20

43 if adam drinks an average of 12 glasses of milk a week for 6 weeks, he will drink about $12 \times 6$ glasses of milk. which of the following is equal to $12 \times 6$?
a $(10 + 6) - (2 + 6)$
b $(10 \times 6) + (2 \times 6)$
c $(10 \times 6) \times (2 \times 6)$
d $(10 + 6) \times (2 + 6)$

Explanation:

Question 41

Step1: Recall exponent definition

An exponent \(a^n\) means multiplying \(a\) by itself \(n\) times. So \(5^3\) means \(5\times5\times5\).

Step2: Calculate the product

\(5\times5 = 25\), then \(25\times5 = 125\).

Step1: Recall exponent definition

\(4^5\) means \(4\times4\times4\times4\times4\).

Step2: Calculate step by step

\(4\times4 = 16\), \(16\times4 = 64\), \(64\times4 = 256\), \(256\times4 = 1024\)? Wait, no, wait: Wait, \(4^1 = 4\), \(4^2 = 16\), \(4^3 = 64\), \(4^4 = 256\), \(4^5 = 1024\)? Wait, no, the options have A as 1024, B as 625 (which is \(5^4\)), C as 256 (\(4^4\)), D as 20. Wait, maybe I miscalculated. Wait, \(4\times4 = 16\), \(16\times4 = 64\), \(64\times4 = 256\), \(256\times4 = 1024\). So \(4^5 = 1024\).

Step1: Recall distributive property

The distributive property states that \(a\times(b + c)=a\times b + a\times c\). Here, \(12 = 10 + 2\), so \(12\times6=(10 + 2)\times6 = 10\times6+2\times6\) (by distributive property).

Step2: Analyze options

• Option A: \((10 + 6)-(2 + 6)=16 - 8 = 8

eq72\) (since \(12\times6 = 72\))

• Option B: \(10\times6+2\times6 = 60 + 12 = 72\), which matches.
• Option C: \((10\times6)\times(2\times6)=60\times12 = 720

eq72\)

• Option D: \((10 + 6)\times(2 + 6)=16\times8 = 128

eq72\)

Answer:

C

Question 42