Select the best answer for the question.
What is $4^3$ in expanded form?
A. $3 \times 3 \times 3 \times 3$
B. $12 \times 12 \times 12$
C. $4 \times 4 \times 4$
D. $8 \times 8$
Answer (2)
4 3 means 4 multiplied by itself 3 times.
This can be written as 4 × 4 × 4 .
Comparing this with the given options, we find that option C matches our result.
Therefore, the answer is C .
Explanation
Understanding the Problem The question asks us to identify the expanded form of 4 3 . This means we need to understand what it means to raise a number to a power.
Understanding Exponents Recall that a b means a multiplied by itself b times. In our case, we have 4 3 , which means 4 multiplied by itself 3 times.
Calculating the Expanded Form Therefore, 4 3 is equivalent to 4 × 4 × 4 . Now we compare this with the given options.
Comparing with Options Option A is 3 × 3 × 3 × 3 , which is 3 4 , not 4 3 .
Option B is 12 × 12 × 12 , which is 1 2 3 . Note that 12 = 4 × 3 , so this is not the same as 4 3 .
Option C is 4 × 4 × 4 , which is exactly what we found for 4 3 .
Option D is 8 × 8 , which is 8 2 . Note that 8 = 2 × 4 , so this is not the same as 4 3 .
Final Answer The correct expanded form of 4 3 is 4 × 4 × 4 . Therefore, the best answer is C.
Examples
Understanding exponents is crucial in many real-world applications. For example, calculating compound interest involves exponents. If you invest money at a certain interest rate, the amount of money you have after a certain number of years can be calculated using an exponential formula. Similarly, exponents are used in calculating population growth, radioactive decay, and many other scientific and engineering applications. Knowing how to expand and simplify exponential expressions is a fundamental skill in mathematics and science.
The correct expanded form of 4 3 is 4 × 4 × 4 , which corresponds to option C. This means that 4 is multiplied by itself three times. The other options do not represent the same value as 4 3 .
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