To determine which of the given exponential forms simplifies to 64, we'll calculate each one step-by-step:
1. Calculate [tex]\((-4)^3\)[/tex]:
[tex]\[
(-4)^3 = (-4) \times (-4) \times (-4) = 16 \times (-4) = -64
\][/tex]
This does not simplify to 64.
2. Calculate [tex]\(2^6\)[/tex]:
[tex]\[
2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64
\][/tex]
This simplifies to 64. So, [tex]\(2^6\)[/tex] is a candidate.
3. Calculate [tex]\(3^4\)[/tex]:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 9 \times 9 = 81
\][/tex]
This does not simplify to 64.
4. Calculate [tex]\((-8)^2\)[/tex]:
[tex]\[
(-8)^2 = (-8) \times (-8) = 64
\][/tex]
This simplifies to 64. So, [tex]\((-8)^2\)[/tex] is also a candidate.
5. Calculate [tex]\((-2)^6\)[/tex]:
[tex]\[
(-2)^6 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2) = 4 \times 4 \times 4 = 64
\][/tex]
This simplifies to 64. So, [tex]\((-2)^6\)[/tex] is also a candidate.
Thus, the original exponential forms that Dawn could have simplified to get a value of 64 are:
- [tex]\(2^6\)[/tex]
- [tex]\((-8)^2\)[/tex]
- [tex]\((-2)^6\)[/tex]
