Which of the following represents \( 5^{4} \) in expanded form? A. \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \) B. \( 5 \cdot 5 \cdot 5 \cdot 5 \) C. \( 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \) D. \( 4 \cdot 4 \cdot 4 \cdot 4 \)
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The correct choice is B. \( 5 \cdot 5 \cdot 5 \cdot 5 \). Expanding \( 5^4 \) means multiplying the base (5) by itself a total of four times. So, in this case, you have four 5s multiplied together, representing the exponent accurately. Now, it’s easy to confuse the exponents! Remember, when you see something like \( a^n \), you're multiplying \( a \) by itself \( n \) times. It can be helpful to practice with smaller numbers to solidify your understanding: for instance, \( 3^2 = 3 \cdot 3 \) and \( 2^3 = 2 \cdot 2 \cdot 2 \). Keep practicing, and soon it will become second nature!