Let's break down the problem step by step to expand and compute the expression [tex]\((-10)^4\)[/tex].
1. Identify the base and exponent:
- The base of the expression is [tex]\(-10\)[/tex].
- The exponent is 4.
2. Understand what the expression means:
- The expression [tex]\((-10)^4\)[/tex] means that we need to multiply [tex]\(-10\)[/tex] by itself 4 times.
3. Expand the expression:
- [tex]\[ (-10)^4 = (-10) \times (-10) \times (-10) \times (-10) \][/tex]
4. First multiplication:
- [tex]\[ (-10) \times (-10) = 100 \][/tex]
- Multiplying two negative numbers results in a positive number.
5. Second multiplication:
- [tex]\[ 100 \times (-10) = -1000 \][/tex]
- Multiplying a positive number by a negative number results in a negative number.
6. Third multiplication:
- [tex]\[ -1000 \times (-10) = 10000 \][/tex]
- Again, multiplying two negative numbers results in a positive number.
Therefore, the final result is:
[tex]\[ (-10)^4 = 10000 \][/tex]
So, expanding and computing [tex]\((-10)^4\)[/tex] gives us [tex]\(10000\)[/tex].
