Question
is the expression 4^10 was simplified using the power rule of exponents, what is an equivalent expanded expression?
A. (4^12)^2
B. (4^5)^2
C. (4^2)^8
D. 4 • 4 • 4 • 4 • 4 • 4 • 4
A. (4^12)^2
B. (4^5)^2
C. (4^2)^8
D. 4 • 4 • 4 • 4 • 4 • 4 • 4
Answers
GPT-4o mini
To find an equivalent expanded expression for \( 4^{10} \) using the power rule of exponents, we can express \( 4^{10} \) in a different form.
The power rule of exponents states that \( (a^m)^n = a^{mn} \). By using this rule, we can break down \( 4^{10} \).
1. **Considering option A: \( (4^{12})^2 \)**
\((4^{12})^2 = 4^{12 \cdot 2} = 4^{24}\), which is not equivalent to \( 4^{10} \).
2. **Considering option B: \( (4^5)^2 \)**
\((4^5)^2 = 4^{5 \cdot 2} = 4^{10}\), which is indeed equivalent to \( 4^{10} \).
3. **Considering option C: \( (4^2)^8 \)**
\((4^2)^8 = 4^{2 \cdot 8} = 4^{16}\), which is not equivalent to \( 4^{10} \).
4. **Considering option D: \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \)**
This is a repeated multiplication of 4, but it only shows 7 multiplications, which yields \( 4^7 \), not \( 4^{10} \).
Thus, the correct answer is **B. \( (4^5)^2 \)**, as it simplifies to \( 4^{10} \).
The power rule of exponents states that \( (a^m)^n = a^{mn} \). By using this rule, we can break down \( 4^{10} \).
1. **Considering option A: \( (4^{12})^2 \)**
\((4^{12})^2 = 4^{12 \cdot 2} = 4^{24}\), which is not equivalent to \( 4^{10} \).
2. **Considering option B: \( (4^5)^2 \)**
\((4^5)^2 = 4^{5 \cdot 2} = 4^{10}\), which is indeed equivalent to \( 4^{10} \).
3. **Considering option C: \( (4^2)^8 \)**
\((4^2)^8 = 4^{2 \cdot 8} = 4^{16}\), which is not equivalent to \( 4^{10} \).
4. **Considering option D: \( 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \)**
This is a repeated multiplication of 4, but it only shows 7 multiplications, which yields \( 4^7 \), not \( 4^{10} \).
Thus, the correct answer is **B. \( (4^5)^2 \)**, as it simplifies to \( 4^{10} \).