Simplify. $$ \frac{27 a b}{63 b c} $$

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UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{27 a b}{63 b c}
$$

**Step 1: Factor the Numbers**

- **27** can be factored into $$ 3 \times 9 $$ or $$ 3^3 $$.
- **63** can be factored into $$ 7 \times 9 $$ or $$ 7 \times 3^2 $$.

**Step 2: Simplify the Fraction**

$$
\frac{27 a b}{63 b c} = \frac{3^3 \cdot a \cdot b}{7 \cdot 3^2 \cdot b \cdot c}
$$

**Step 3: Cancel Common Factors**

- **$$ b $$** appears in both the numerator and the denominator, so it cancels out.
- **$$ 3^2 $$** in the denominator cancels with part of **$$ 3^3 $$** in the numerator, leaving one **3** in the numerator.

$$
\frac{3 \cdot a}{7 \cdot c} = \frac{3a}{7c}
$$

**Final Simplified Form:**

$$
\frac{3a}{7c}
$$
$$ \frac{3a}{7c} $$

Simplify.

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