isabella292008
Answered

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Choose the correct simplification of the expression [tex]\left(\frac{2 b}{c}\right)^3[/tex].

A. [tex]\frac{2 b^3}{c^3}[/tex]
B. [tex]\frac{8 b^3}{c^3}[/tex]
C. [tex]\frac{2 b^3}{c}[/tex]
D. [tex]\frac{2 b}{c^3}[/tex]

Sagot :

GinnyAnswer
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]
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