Question
if the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression?
A.(4^5)^2
B. 4 x 4 x 4 x 4 x 4 x 4 x 4
C. (4^2)^8
D. (4^12)^2
A.(4^5)^2
B. 4 x 4 x 4 x 4 x 4 x 4 x 4
C. (4^2)^8
D. (4^12)^2
Answers
GPT-4o mini
To simplify \(4^{10}\) using the Power Rule of Exponents, we can express it in other equivalent forms. The Power Rule states that \((a^m)^n = a^{m \cdot n}\).
Let's analyze each option to see if it generates \(4^{10}\):
A. \((4^5)^2\): Using the Power Rule, this simplifies to \(4^{5 \cdot 2} = 4^{10}\). This option is equivalent.
B. \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\): This expression equals \(4^7\) (since it has seven 4's). This is not equivalent to \(4^{10}\).
C. \((4^2)^8\): Using the Power Rule, this simplifies to \(4^{2 \cdot 8} = 4^{16}\). This is not equivalent to \(4^{10}\).
D. \((4^{12})^2\): Using the Power Rule, this simplifies to \(4^{12 \cdot 2} = 4^{24}\). This is not equivalent to \(4^{10}\).
Thus, the only option that simplifies correctly to \(4^{10}\) is:
**A. (4^5)^2**
Let's analyze each option to see if it generates \(4^{10}\):
A. \((4^5)^2\): Using the Power Rule, this simplifies to \(4^{5 \cdot 2} = 4^{10}\). This option is equivalent.
B. \(4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\): This expression equals \(4^7\) (since it has seven 4's). This is not equivalent to \(4^{10}\).
C. \((4^2)^8\): Using the Power Rule, this simplifies to \(4^{2 \cdot 8} = 4^{16}\). This is not equivalent to \(4^{10}\).
D. \((4^{12})^2\): Using the Power Rule, this simplifies to \(4^{12 \cdot 2} = 4^{24}\). This is not equivalent to \(4^{10}\).
Thus, the only option that simplifies correctly to \(4^{10}\) is:
**A. (4^5)^2**