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38 which of the following is equal to $6^7$? a $6 \\times 7$ b $6 \\tim…

Question

38 which of the following is equal to $6^7$?
a $6 \times 7$
b $6 \times 6 \times 6 \times 6 \times 6 \times 6$
c $7 \times 7 \times 7 \times 7 \times 7 \times 7$
d $6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6$

39 a huge metal container in teddys backyard forms a perfect cube. its length, width, and height are each 4 feet. if it rains enough to fill the container, there will be $4^3$ cubic feet of water in it. which of the following is equal to $4^3$?
a 256
b 64
c 27
d 12

40 which of the following is equal to $3^6$?
a $3 \times 6$
b $6 \times 6 \times 6$
c $3 \times 3 \times 3 \times 3 \times 3 \times 3$
d $3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$

Explanation:

Response
Question 38

Step1: Recall exponent definition

An exponent \(a^n\) means multiplying \(a\) by itself \(n\) times. For \(6^7\), the base is 6 and the exponent is 7.

Step2: Analyze options

  • Option A: \(6\times7\) is multiplication of 6 and 7, not exponentiation.
  • Option B: \(6\times6\times6\times6\times6\times6\) is \(6^6\) (6 multiplied 6 times), not \(6^7\).
  • Option C: \(7\times7\times7\times7\times7\times7\) is \(7^6\) (base 7, exponent 6), not related to \(6^7\).
  • Option D: \(6\times6\times6\times6\times6\times6\times6\) is 6 multiplied by itself 7 times, which is \(6^7\).

Step1: Recall exponent definition

\(a^n\) means \(a\) multiplied by itself \(n\) times. For \(4^3\), base is 4, exponent is 3.

Step2: Calculate \(4^3\)

\(4^3 = 4\times4\times4 = 16\times4 = 64\).

Step3: Analyze options

  • Option A: 256 is \(4^4 = 4\times4\times4\times4 = 256\), not \(4^3\).
  • Option B: 64 is \(4^3\) as calculated.
  • Option C: 27 is \(3^3 = 3\times3\times3 = 27\), not \(4^3\).
  • Option D: 12 is not a power of 4.

Step1: Recall exponent definition

\(a^n\) means \(a\) multiplied by itself \(n\) times. For \(3^6\), base is 3, exponent is 6.

Step2: Analyze options

  • Option A: \(3\times6\) is multiplication of 3 and 6, not exponentiation.
  • Option B: \(6\times6\times6\) is \(6^3\), base 6, not 3.
  • Option C: \(3\times3\times3\times3\times3\times3\) is 3 multiplied by itself 6 times, which is \(3^6\).
  • Option D: \(3\times3\times3\times3\times3\times3\times3\) is \(3^7\) (3 multiplied 7 times), not \(3^6\).

Answer:

D. \(6\times6\times6\times6\times6\times6\times6\)

Question 39