Select the three expressions that are equivalent to
\[4^{10}\].
Choose 3 answers:
Choose 3 answers:
(Choice A)
\[(4^5)^2\]
A
\[(4^5)^2\]
(Choice B)
\[10\cdot 10\cdot 10\cdot 10\]
B
\[10\cdot 10\cdot 10\cdot 10\]
(Choice C)
\[\dfrac{4^{20}}{4^{10}}\]
C
\[\dfrac{4^{20}}{4^{10}}\]
(Choice D)
\[4^2 \cdot 4^5\]
D
\[4^2 \cdot 4^5\]
(Choice E)
\[(4^2\cdot 4^3)^2\]
E
\[(4^2\cdot 4^3)^2\]
The three expressions that are equivalent to $4^{10}$ are $\boxed{\text{(A)}, \text{(B)}, \text{(D)}}$.
only A was correct
To solve this question, we need to determine which expressions are equivalent to \(4^{10}\).
First, let's simplify each choice:
A. \((4^5)^2\) can be simplified as \(4^{10}\), so it is equivalent to the given expression.
B. \(10 \cdot 10 \cdot 10 \cdot 10\) is equal to \(10^4\), not \(4^{10}\).
C. \(\dfrac{4^{20}}{4^{10}}\) can be simplified as \(4^{20-10} = 4^{10}\), so it is equivalent to the given expression.
D. \(4^2 \cdot 4^5 = 4^{2+5} = 4^7\), not \(4^{10}\).
E. \((4^2 \cdot 4^3)^2 = (4^5)^2\) can be simplified as \(4^{10}\), so it is equivalent to the given expression.
Therefore, the three expressions that are equivalent to \(4^{10}\) are:
- (Choice A) \((4^5)^2\)
- (Choice C) \(\dfrac{4^{20}}{4^{10}}\)
- (Choice E) \((4^2 \cdot 4^3)^2\)