To solve the expression [tex]\((-1)^5\)[/tex], follow these steps:
1. Identify the base and the exponent: The base in this expression is [tex]\(-1\)[/tex] and the exponent is [tex]\(5\)[/tex].
2. Understand the property of negative numbers raised to exponents:
- When a negative number is raised to an odd exponent, the result is negative.
- When a negative number is raised to an even exponent, the result is positive.
3. Examine the exponent: In this case, the exponent is [tex]\(5\)[/tex], which is an odd number.
4. Apply the property of exponents: Since the exponent [tex]\(5\)[/tex] is odd, [tex]\((-1)\)[/tex] raised to the power of [tex]\(5\)[/tex] will result in [tex]\(-1\)[/tex].
Thus,
[tex]\[ (-1)^5 = -1 \][/tex]
So, the value of the expression [tex]\((-1)^5\)[/tex] is [tex]\(-1\)[/tex].
