To evaluate [tex]\(\left(-\frac{1}{3}\right)^3\)[/tex], let's break down the steps involved in this calculation.
1. Identify the base and the exponent:
The given expression is [tex]\(\left(-\frac{1}{3}\right)^3\)[/tex]. Here, [tex]\(-\frac{1}{3}\)[/tex] is the base and [tex]\(3\)[/tex] is the exponent.
2. Understand what the exponent means:
The exponent [tex]\(3\)[/tex] indicates that the base [tex]\(-\frac{1}{3}\)[/tex] should be multiplied by itself three times. So, we have:
[tex]\[
\left(-\frac{1}{3}\right)^3 = \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right)
\][/tex]
3. Perform the multiplication:
- First, multiply [tex]\(\left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right)\)[/tex]:
[tex]\[
\left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) = \frac{1}{3} \times \frac{1}{3} = \frac{1 \cdot 1}{3 \cdot 3} = \frac{1}{9}
\][/tex]
Notice that the product of two negative numbers is positive.
- Next, multiply the result by [tex]\(\left(-\frac{1}{3}\right)\)[/tex]:
[tex]\[
\frac{1}{9} \times \left(-\frac{1}{3}\right) = \frac{1 \times (-1)}{9 \times 3} = \frac{-1}{27}
\][/tex]
4. Express the final result:
Therefore, [tex]\(\left(-\frac{1}{3}\right)^3 = \frac{-1}{27}\)[/tex].
5. Convert the fraction to a decimal (if needed):
[tex]\[
\frac{-1}{27} \approx -0.03703703703703703
\][/tex]
So, the evaluated result of [tex]\(\left(-\frac{1}{3}\right)^3\)[/tex] is [tex]\(\boxed{-0.03703703703703703}\)[/tex].
