To simplify the expression [tex]\(\left(\frac{3}{6}\right)^3\)[/tex]:
1. Simplify the Fraction [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\frac{3}{6} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{3}{6}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].
2. Raise the Simplified Fraction to the Power of 3:
[tex]\[
\left(\frac{1}{2}\right)^3
\][/tex]
3. Calculate [tex]\(\left(\frac{1}{2}\right)^3\)[/tex]:
- When we raise a fraction to a power, we raise both the numerator and the denominator to that power.
- The numerator is [tex]\(1\)[/tex] raised to the power of [tex]\(3\)[/tex], which is [tex]\(1^3 = 1\)[/tex].
- The denominator is [tex]\(2\)[/tex] raised to the power of [tex]\(3\)[/tex], which is [tex]\(2^3 = 8\)[/tex].
Therefore,
[tex]\[
\left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8}
\][/tex]
So, [tex]\(\left(\frac{3}{6}\right)^3\)[/tex] simplifies to [tex]\(\frac{1}{8}\)[/tex].
In decimal form:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
[tex]\[
\left(0.5\right)^3 = 0.125
\][/tex]
The simplified result of [tex]\(\left(\frac{3}{6}\right)^3\)[/tex] is [tex]\(\frac{1}{8}\)[/tex] or [tex]\(0.125\)[/tex].
