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Simplify the following expression:

[tex]\ \textless \ br/\ \textgreater \ \frac{p^2 q^2 r^2}{a^2 b^2} \times \frac{3 a^3 b^3}{4 p^2 q^2 r^3}\ \textless \ br/\ \textgreater \ [/tex]

Sagot :

GinnyAnswer
Let's simplify the expression step by step:

[tex]\[ \frac{p^2 q^2 r^2}{a^2 b^2} \times \frac{3 a^3 b^3}{4 p^2 q^2 r^3} \][/tex]

1. Combine the fractions by multiplying the numerators together and the denominators together:

[tex]\[ \frac{(p^2 q^2 r^2) \cdot (3 a^3 b^3)}{(a^2 b^2) \cdot (4 p^2 q^2 r^3)} \][/tex]

2. Distribute the multiplication in the numerator and the denominator:

Numerator:

[tex]\[ (p^2 q^2 r^2) \cdot (3 a^3 b^3) = 3 p^2 q^2 r^2 a^3 b^3 \][/tex]

Denominator:

[tex]\[ (a^2 b^2) \cdot (4 p^2 q^2 r^3) = 4 a^2 b^2 p^2 q^2 r^3 \][/tex]

Now the expression is:

[tex]\[ \frac{3 p^2 q^2 r^2 a^3 b^3}{4 a^2 b^2 p^2 q^2 r^3} \][/tex]

3. Cancel out the common terms in the numerator and the denominator:

- [tex]\(p^2\)[/tex] in the numerator cancels with [tex]\(p^2\)[/tex] in the denominator.
- [tex]\(q^2\)[/tex] in the numerator cancels with [tex]\(q^2\)[/tex] in the denominator.
- [tex]\(r^2\)[/tex] in the numerator partially cancels with [tex]\(r^3\)[/tex] in the denominator, leaving [tex]\(r\)[/tex] in the denominator.
- [tex]\(a^2\)[/tex] in the denominator cancels with [tex]\(a^2\)[/tex] (part of [tex]\(a^3\)[/tex]) in the numerator, leaving [tex]\(a\)[/tex] in the numerator.
- [tex]\(b^2\)[/tex] in the denominator cancels with [tex]\(b^2\)[/tex] (part of [tex]\(b^3\)[/tex]) in the numerator, leaving [tex]\(b\)[/tex] in the numerator.

So, the expression reduces to:

[tex]\[ \frac{3 a b}{4 r} \][/tex]

Therefore, the simplified expression is:

[tex]\[ \boxed{\frac{3 a b}{4 r}} \][/tex]
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