To solve the expression [tex]\((-4)^5\)[/tex], you need to raise [tex]\(-4\)[/tex] to the power of 5. Here is a step-by-step breakdown of how you can do that:
1. Understand the Base and Exponent:
- The base is [tex]\(-4\)[/tex].
- The exponent is 5.
- Raising a number to an exponent means multiplying the base by itself as many times as the value of the exponent.
2. Multiply Step-by-Step:
- First, [tex]\((-4)\)[/tex] to the power of 5 means multiplying [tex]\(-4\)[/tex] by itself five times.
- [tex]\((-4) \times (-4) \times (-4) \times (-4) \times (-4)\)[/tex]
3. Calculate Each Step of Multiplication:
- Multiply the first two [tex]\(-4\)[/tex]'s:
[tex]\[
(-4) \times (-4) = 16
\][/tex]
- Multiply the result by the next [tex]\(-4\)[/tex]:
[tex]\[
16 \times (-4) = -64
\][/tex]
- Multiply the result by the next [tex]\(-4\)[/tex]:
[tex]\[
-64 \times (-4) = 256
\][/tex]
- Finally, multiply the result by the last [tex]\(-4\)[/tex]:
[tex]\[
256 \times (-4) = -1024
\][/tex]
4. Final Result:
- After multiplying [tex]\(-4\)[/tex] by itself five times, you end up with [tex]\(-1024\)[/tex].
Thus, the value of [tex]\((-4)^5\)[/tex] is [tex]\(-1024\)[/tex].
