12. $$ -6\left(\frac{2}{3} p^{8}\right)^{3} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
-6\left(\frac{2}{3} p^{8}\right)^{3}
$$

Follow these steps:

1. **Apply the exponent to both the coefficient and the variable:**

$$
\left(\frac{2}{3} p^{8}\right)^{3} = \left(\frac{2}{3}\right)^{3} \cdot \left(p^{8}\right)^{3}
$$

2. **Calculate each part separately:**

$$
\left(\frac{2}{3}\right)^{3} = \frac{2^3}{3^3} = \frac{8}{27}
$$
$$
\left(p^{8}\right)^{3} = p^{8 \times 3} = p^{24}
$$

So,

$$
\left(\frac{2}{3} p^{8}\right)^{3} = \frac{8}{27} p^{24}
$$

3. **Multiply by -6:**

$$
-6 \cdot \frac{8}{27} p^{24} = -\frac{48}{27} p^{24}
$$

4. **Simplify the fraction by dividing numerator and denominator by 3:**

$$
-\frac{48 \div 3}{27 \div 3} p^{24} = -\frac{16}{9} p^{24}
$$

**Final Simplified Expression:**

$$
-\frac{16}{9} p^{24}
$$
$$ -\frac{16}{9} p^{24} $$

Solución de inteligencia artificial de Upstudy