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Jeff is working with numbers that are cubed and he is confused. He says that \( 0^{3}=0 \) and \( 2^{3} \) equals 6, so \( 5^{3} \) must be 15 . What does Jeff think the rule for exponents is? What manipulative (a physical object) can you draw to show Jeff a representation of each of the first five cube numbers? Choose the correct answer below. Use the Show Work feature to provide related calculations and additional reasoning to support your answer. A. Jeff is multiplying a number of bases indicated by the exponent, which is the correct procedure. B. Jeff is multiplying the base by the exponent, which is an incorrect procedure. In this case, he is multiplying by three, not taking numbers to the third power. C. Jeff is adding the base and the exponent, which is an incorrect procedure. In this case, he is adding three, not taking numbers to the third power. D. Jeff is adding the product of the base and the exponent to the base, which is an incorrect procedure. In this case, he is adding three times the numbers, not takine numbers to the third power.

Ask by Parsons Sherman. in the United States
Mar 16,2025

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Jeff thinks that to find \( x^3 \), you multiply the base by 3. However, the correct method is to multiply the base by itself three times. To show him, use unit cubes to build cubes for each number: 0, 1, 8, 27, and 64. This demonstrates that \( x^3 \) means multiplying the base by itself three times, not just multiplying by 3.

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Mind Expander

B. Jeff is multiplying the base by the exponent, which is an incorrect procedure. In this case, he is multiplying by three, not taking numbers to the third power. Cubing a number means multiplying the number by itself two more times (e.g., \( 2^3 = 2 \times 2 \times 2 = 8 \)), but Jeff mistakenly interpreted it as \( 2 \times 3 = 6 \). To show Jeff the representation of each of the first five cube numbers, you could use small blocks or cubes. For instance, you can stack 1 cube for \( 1^3 \), 8 cubes arranged in an 2x2x2 formation for \( 2^3 \), 27 cubes for \( 3^3 \)(3x3x3), 64 cubes for \( 4^3 \), and 125 cubes for \( 5^3 \). These physical representations will help him visualize how the cubing process works!

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