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Simplify [tex]\frac{3 y^4}{9 y^7}[/tex].

A. [tex]\frac{3}{y^3}[/tex]

B. [tex]\frac{1}{3 y^3}[/tex]

C. [tex]3 y^3[/tex]

D. [tex]\frac{y^3}{3}[/tex]

Sagot :

GinnyAnswer
To simplify the given expression [tex]\(\frac{3 y^4}{9 y^7}\)[/tex], we can follow these steps:

1. Factor the constants:
[tex]\[ \frac{3 y^4}{9 y^7} = \frac{3}{9} \cdot \frac{y^4}{y^7} \][/tex]

2. Simplify the fraction of constants:
[tex]\[ \frac{3}{9} = \frac{1}{3} \][/tex]

3. Simplify the fraction of the powers of [tex]\(y\)[/tex]:
[tex]\[ \frac{y^4}{y^7} = y^{4-7} = y^{-3} \][/tex]

4. Combine the simplified parts:
[tex]\[ \frac{3 y^4}{9 y^7} = \frac{1}{3} \cdot y^{-3} \][/tex]

5. Rewrite [tex]\(y^{-3}\)[/tex] as [tex]\(\frac{1}{y^3}\)[/tex]:
[tex]\[ \frac{1}{3} \cdot y^{-3} = \frac{1}{3 y^3} \][/tex]

Thus, the simplified form of [tex]\(\frac{3 y^4}{9 y^7}\)[/tex] is [tex]\(\frac{1}{3 y^3}\)[/tex].

Therefore, the correct answer is:
[tex]\(\boxed{\frac{1}{3 y^3}}\)[/tex]
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