If the expression 4 10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)

Question

Responses

4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4

(4 2) 8
left parenthesis 4 squared right parenthesis superscript 8 baseline

(4 5) 2
left parenthesis 4 superscript 5 baseline right parenthesis squared

(4 12) 2
left parenthesis 4 superscript 12 baseline right parenthesis squared

Answer 1

To simplify the expression $4^{10}$ using the Power Rule of Exponents, we need to recognize that we can express $4^{10}$ in terms of its prime factorization. Specifically, $4$ can be rewritten as $4^1$.

The Power Rule states that $(a^m{)}^n=a^{m\cdot n}$. Thus, if we rewrite $4$ in terms of its power, we have $4=4^1$.

However, for one of the provided options to be equivalent to $4^{10}$, we must check if any transformation matches $4^{10}$.

Let's analyze the options:

1. $4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4$: This translates to $4^7$, which is not $4^{10}$.

2. $(4^2{)}^8$: Using the Power Rule, this simplifies to $4^{2\cdot 8}=4^{16}$, which is not $4^{10}$.

3. $(4^5{)}^2$: This simplifies to $4^{5\cdot 2}=4^{10}$, which is correct.

4. $(4^{12}{)}^2$: This simplifies to $4^{12\cdot 2}=4^{24}$, which is not $4^{10}$.

Therefore, the correct choice that is equivalent to $4^{10}$ is:

$(4^5{)}^2$.