Answer :

Let's solve the expression step-by-step:

We need to simplify the expression [tex]\(\frac{5 y^9}{21 x^9 y^6} \cdot 33 x^9 y^4\)[/tex].

Step 1: Simplify the expression

Start with the expression:

[tex]\[
\frac{5 y^9}{21 x^9 y^6} \cdot 33 x^9 y^4
\][/tex]

1. Combine the fractions:

[tex]\[
\left(\frac{5 y^9}{21 x^9 y^6}\right) \cdot (33 x^9 y^4) = \frac{5 \times 33 \times y^9 \times x^9 \times y^4}{21 \times x^9 \times y^6}
\][/tex]

2. Multiply the numerators and denominators:

[tex]\[
= \frac{165 \times y^{13} \times x^9}{21 \times x^9 \times y^6}
\][/tex]

Here, [tex]\(y^{13}\)[/tex] comes from [tex]\(y^9 \times y^4\)[/tex] as we combine the powers of [tex]\(y\)[/tex].

3. Cancel out [tex]\(x^9\)[/tex] in the numerator and denominator:

[tex]\[
= \frac{165 \times y^{13}}{21 \times y^6}
\][/tex]

Step 2: Simplify the powers of [tex]\(y\)[/tex]:

Subtract the exponent in the denominator from the exponent in the numerator:

[tex]\[
y^{13 - 6} = y^7
\][/tex]

So the expression simplifies to:

[tex]\[
= \frac{165}{21} \times y^7
\][/tex]

Step 3: Simplify the coefficient [tex]\(\frac{165}{21}\)[/tex]:

Both 165 and 21 can be divided by 3:

- Divide 165 by 3: [tex]\(165 \div 3 = 55\)[/tex]
- Divide 21 by 3: [tex]\(21 \div 3 = 7\)[/tex]

Thus, [tex]\(\frac{165}{21}\)[/tex] simplifies to [tex]\(\frac{55}{7}\)[/tex].

Final Simplified Expression:

Thus, the final simplified expression is:

[tex]\[
\frac{55}{7} \times y^7
\][/tex]

So the simplified result is [tex]\(\frac{55}{7} y^7\)[/tex].

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Rewritten by : Barada