To simplify the expression [tex]\(\left(\frac{2b}{c}\right)^3\)[/tex], let's go through the steps:
1. Start with the given expression:
[tex]\[
\left(\frac{2b}{c}\right)^3
\][/tex]
2. Apply the cube to both the numerator [tex]\(2b\)[/tex] and the denominator [tex]\(c\)[/tex]:
[tex]\[
\left(\frac{2b}{c}\right)^3 = \frac{(2b)^3}{c^3}
\][/tex]
3. Calculate [tex]\((2b)^3\)[/tex]:
[tex]\[
(2b)^3 = 2^3 \cdot b^3
\][/tex]
4. Simplify the powers:
[tex]\[
2^3 = 8
\][/tex]
5. Combine the terms to obtain:
[tex]\[
\frac{8b^3}{c^3}
\][/tex]
Thus, the correct simplification of the expression [tex]\(\left(\frac{2b}{c}\right)^3\)[/tex] is:
[tex]\[
\boxed{\frac{8b^3}{c^3}}
\][/tex]
