Let's solve the expression step-by-step.
1. Start with the given power: [tex]\[ (-4)^{-3} \][/tex]
2. Apply the negative exponents rule: [tex]\[ (-4)^{-3} = \frac{1}{(-4)^3} \][/tex]
3. Now, calculate [tex]\((-4)^3\)[/tex]. To do this, expand the exponent:
[tex]\[ (-4)^3 = (-4) \times (-4) \times (-4) \][/tex]
4. Simplify the multiplication step-by-step:
- Multiply the first two factors: [tex]\[ (-4) \times (-4) = 16 \][/tex]
- Then, multiply the result by the third factor: [tex]\[ 16 \times (-4) = -64 \][/tex]
5. Therefore, [tex]\((-4)^3 = -64\)[/tex], so we can substitute this back into our fraction: [tex]\[ \frac{1}{(-4)^3} = \frac{1}{-64} \][/tex]
6. The value of [tex]\(\frac{1}{-64}\)[/tex] is:
[tex]\[ -\frac{1}{64} \][/tex]
So, the value of [tex]\((-4)^{-3}\)[/tex] is [tex]\(-\frac{1}{64}\)[/tex]. The correct answer is:
[tex]\[ -\frac{1}{64} \][/tex]
